Nineteen papers published by Geometry & Topology Publications

Fifteen papers have been published by Algebraic & Geometric Topology

(1) Algebraic & Geometric Topology 7 (2007) 1441-1470
Dendroidal sets
by Ieke Moerdijk and Ittay Weiss
URL: http://www.msp.warwick.ac.uk/agt/2007/07/p056.xhtml
DOI: 10.2140/agt.2007.7.1441

(2) Algebraic & Geometric Topology 7 (2007) 1561-1578
Covering a nontaming knot by the unlink
by Michael H Freedman and David Gabai
URL: http://www.msp.warwick.ac.uk/agt/2007/07/p062.xhtml
DOI: 10.2140/agt.2007.7.1561

(3) Algebraic & Geometric Topology 7 (2007) 1579-1598
Mutant knots and intersection graphs
by Sergei V Chmutov and Sergei K Lando
URL: http://www.msp.warwick.ac.uk/agt/2007/07/p063.xhtml
DOI: 10.2140/agt.2007.7.1579

(4) Algebraic & Geometric Topology 7 (2007) 1599-1632
A sufficient condition for a branched surface to fully carry a lamination
by Skander Zannad
URL: http://www.msp.warwick.ac.uk/agt/2007/07/p064.xhtml
DOI: 10.2140/agt.2007.7.1599

(5) Algebraic & Geometric Topology 7 (2007) 1633-1650
On the multiplicative structure of topological Hochschild homology
by Morten Brun, Zbigniew Fiedorowicz and Rainer M Vogt
URL: http://www.msp.warwick.ac.uk/agt/2007/07/p065.xhtml
DOI: 10.2140/agt.2007.7.1633

(6) Algebraic & Geometric Topology 7 (2007) 1651-1697
Finite abelian subgroups of the mapping class group
by S Allen Broughton and Aaron Wootton
URL: http://www.msp.warwick.ac.uk/agt/2007/07/p066.xhtml
DOI: 10.2140/agt.2007.7.1651

(7) Algebraic & Geometric Topology 7 (2007) 1699-1765
An algebraic model for the loop space homology of a homotopy fiber
by Kathryn Hess and Ran Levi
URL: http://www.msp.warwick.ac.uk/agt/2007/07/p067.xhtml
DOI: 10.2140/agt.2007.7.1699

(8) Algebraic & Geometric Topology 7 (2007) 1767-1790
Congruence and quantum invariants of 3-manifolds
by Patrick M Gilmer
URL: http://www.msp.warwick.ac.uk/agt/2007/07/p068.xhtml
DOI: 10.2140/agt.2007.7.1767

(9) Algebraic & Geometric Topology 7 (2007) 1791-1804
A parametrized Borsuk-Ulam theorem for a product of spheres with
free Z_p-action and free S^1-action
by Denise de Mattos and Edivaldo L dos Santos
URL: http://www.msp.warwick.ac.uk/agt/2007/07/p069.xhtml
DOI: 10.2140/agt.2007.7.1791

(10) Algebraic & Geometric Topology 7 (2007) 1805-1808
Lusternik-Schnirelmann category of spaces with free fundamental group
by Jeff Strom
URL: http://www.msp.warwick.ac.uk/agt/2007/07/p070.xhtml
DOI: 10.2140/agt.2007.7.1805

(11) Algebraic & Geometric Topology 7 (2007) 1809-1919
Chevalley p-local finite groups
by Carles Broto and Jesper M Møller
URL: http://www.msp.warwick.ac.uk/agt/2007/07/p071.xhtml
DOI: 10.2140/agt.2007.7.1809

(12) Algebraic & Geometric Topology 7 (2007) 1921-1948
Pseudo-Anosov homeomorphisms and the lower central series of a
surface group
by Justin Malestein
URL: http://www.msp.warwick.ac.uk/agt/2007/07/p072.xhtml
DOI: 10.2140/agt.2007.7.1921

(13) Algebraic & Geometric Topology 7 (2007) 1949-1962
Lens spaces obtainable by surgery on doubly primitive knots
by Kazuhiro Ichihara and Toshio Saito
URL: http://www.msp.warwick.ac.uk/agt/2007/07/p073.xhtml
DOI: 10.2140/agt.2007.7.1949

(14) Algebraic & Geometric Topology 7 (2007) 1963-1977
The homotopy infinite symmetric product represents stable homotopy
by Christian Schlichtkrull
URL: http://www.msp.warwick.ac.uk/agt/2007/07/p074.xhtml
DOI: 10.2140/agt.2007.7.1963

(15) Algebraic & Geometric Topology 7 (2007) 1979-1986
Non-finiteness results for Nil-groups
by Joachim Grunewald
URL: http://www.msp.warwick.ac.uk/agt/2007/07/p075.xhtml
DOI: 10.2140/agt.2007.7.1979

Four papers have been published by Geometry & Topology

(16) Geometry & Topology 11 (2007) 2265-2276
On the virtual Betti numbers of arithmetic hyperbolic 3-manifolds
by D Cooper, D D Long and A W Reid
URL: http://www.msp.warwick.ac.uk/gt/2007/11/p047.xhtml
DOI: 10.2140/gt.2007.11.2265

(17) Geometry & Topology 11 (2007) 2277-2338
Knot Floer homology of Whitehead doubles
by Matthew Hedden
URL: http://www.msp.warwick.ac.uk/gt/2007/11/p048.xhtml
DOI: 10.2140/gt.2007.11.2277

(18) Geometry & Topology 11 (2007) 2339-2412
On combinatorial link Floer homology
by Ciprian Manolescu, Peter Ozsvath, Zoltan Szabo and Dylan Thurston
URL: http://www.msp.warwick.ac.uk/gt/2007/11/p049.xhtml
DOI: 10.2140/gt.2007.11.2339

(19) Geometry & Topology 11 (2007) 2413-2440
Flexing closed hyperbolic manifolds.
by D Cooper, D D Long and M B Thistlethwaite
URL: http://www.msp.warwick.ac.uk/gt/2007/11/p050.xhtml
DOI: 10.2140/gt.2007.11.2413

Abstracts follow

(1) Dendroidal sets
by Ieke Moerdijk and Ittay Weiss

We introduce the concept of a dendroidal set. This is a generalization
of the notion of a simplicial set, specially suited to the study of
(coloured) operads in the context of homotopy theory. We define a
category of trees, which extends the category Delta used in simplicial
sets, whose presheaf category is the category of dendroidal sets. We
show that there is a closed monoidal structure on dendroidal sets which
is closely related to the Boardman-Vogt tensor product of (coloured)
operads. Furthermore, we show that each (coloured) operad in a suitable
model category has a coherent homotopy nerve which is a dendroidal set,
extending another construction of Boardman and Vogt. We also define
a notion of an inner Kan dendroidal set, which is closely related to
simplicial Kan complexes. Finally, we briefly indicate the theory of
dendroidal objects in more general monoidal categories, and outline
several of the applications and further theory of dendroidal sets.


(2) Covering a nontaming knot by the unlink
by Michael H Freedman and David Gabai

There exists an open 3-manifold M and a simple closed curve gamma in
M such that pi_1(M-gamma) is infinitely generated, pi_1(M) is finitely
generated and the preimage of gamma in the universal covering of M is
equivalent to the standard locally finite set of vertical lines in R^3,
that is, the trivial link of infinitely many components in R^3.


(3) Mutant knots and intersection graphs
by Sergei V Chmutov and Sergei K Lando

We prove that if a finite order knot invariant does not distinguish mutant
knots, then the corresponding weight system depends on the intersection
graph of a chord diagram rather than on the diagram itself. Conversely,
if we have a weight system depending only on the intersection graphs of
chord diagrams, then the composition of such a weight system with the
Kontsevich invariant determines a knot invariant that does not distinguish
mutant knots. Thus, an equivalence between finite order invariants not
distinguishing mutants and weight systems depending only on intersections
graphs is established. We discuss the relationship between our results
and certain Lie algebra weight systems.


(4) A sufficient condition for a branched surface to fully carry a lamination
by Skander Zannad

We give a sufficient condition for a branched surface in a 3 dimensional
manifold to fully carry a lamination, giving a piece of answer to a
classical question of D Gabai.


(5) On the multiplicative structure of topological Hochschild homology
by Morten Brun, Zbigniew Fiedorowicz and Rainer M Vogt

We show that the topological Hochschild homology THH(R) of an E_n-ring
spectrum R is an E_{n-1}-ring spectrum. The proof is based on the fact
that the tensor product of the operad Ass for monoid structures and
the little n-cubes operad is an E_{n+1}-operad, a result which is of
independent interest.


(6) Finite abelian subgroups of the mapping class group
by S Allen Broughton and Aaron Wootton

The problem of enumeration of conjugacy classes of finite abelian
subgroups of the mapping class group M_{sigma} of a closed, smooth,
orientable surface S of genus sigma at least 2 is considered. A complete
method of enumeration is achieved for finite elementary abelian subgroups
and steps are taken toward enumeration of finite abelian subgroups.


(7) An algebraic model for the loop space homology of a homotopy fiber
by Kathryn Hess and Ran Levi

Let F denote the homotopy fiber of a map f: K -> L of 2-reduced simplicial
sets. Using as input data the strongly homotopy coalgebra structure of the
chain complexes of K and L, we construct a small, explicit chain algebra,
the homology of which is isomorphic as a graded algebra to the homology
of GF, the simplicial (Kan) loop group on F. To construct this model,
we develop machinery for modeling the homotopy fiber of a morphism of
chain Hopf algebras.

Essential to our construction is a generalization of the operadic
description of the category DCSH of chain coalgebras and of
strongly homotopy coalgebra maps given in [Hess--Parent--Scott
arXiv:math.AT/0505559] to strongly homotopy morphisms of comodules over
Hopf algebras. This operadic description is expressed in terms of a
general theory of monoidal structures in categories with morphism sets
parametrized by co-rings, which we elaborate


(8) Congruence and quantum invariants of 3-manifolds
by Patrick M Gilmer

Let f be an integer greater than one. We study three progressively
finer equivalence relations on closed 3-manifolds generated by Dehn
surgery with denominator f: weak f-congruence, f-congruence, and
strong f-congruence. If f is odd, weak f-congruence preserves the ring
structure on cohomology with Z_f-coefficients. We show that strong
f-congruence coincides with a relation previously studied by Lackenby.
Lackenby showed that the quantum SU(2) invariants are well-behaved under
this congruence. We strengthen this result and extend it to the SO(3)
quantum invariants. We also obtain some corresponding results for the
coarser equivalence relations, and for quantum invariants associated to
more general modular categories. We compare S^3, the Poincar\'{e} homology
sphere, the Brieskorn homology sphere Sigma(2,3,7) and their mirror
images up to strong f-congruence. We distinguish the weak f-congruence
classes of some manifolds with the same Z_f-cohomology ring structure.


(9) A parametrized Borsuk-Ulam theorem for a product of spheres with
free Z_p-action and free S^1-action
by Denise de Mattos and Edivaldo L dos Santos

In this paper, we prove parametrized Borsuk--Ulam theorems for
bundles whose fibre has the same cohomology (mod p) of a product
of spheres with any free Z_p-action and for bundles whose fibre has
rational cohomology ring isomorphic to the rational cohomology ring of
a product of spheres with any free S^1-action. These theorems extend the
result proved by Koikara and Mukerjee [Topology Appl. 63 (1995) 39-52].
Further, in the particular case where G=Z_p, we estimate the ``size"
of the Z_p-coincidence set of a fibre-preserving map.


(10) Lusternik-Schnirelmann category of spaces with free fundamental group
by Jeff Strom

We find upper bounds for the Lusternik-Schnirelmann category of
spaces with free fundamental groups. We prove, in particular, that
if X is a finite-dimensional CW complex with a free fundamental
group, then cat(X) <= (2/3)dim(X)+1. Our results specialize to
resolve a question about the LS category of manifolds posed by
Dranishnikov, Katz and Rudyak.


(11) Chevalley p-local finite groups
by Carles Broto and Jesper M M&oslash;ller

We describe the spaces of homotopy fixed points of unstable Adams
operations acting on p-compact groups and also of unstable Adams
operations twisted with a finite order automorphism of the p-compact
group. We obtain new exotic p-local finite groups.


(12) Pseudo-Anosov homeomorphisms and the lower central series of a
surface group
by Justin Malestein

Let Gamma_k be the lower central series of a surface group Gamma of
a compact surface S with one boundary component. A simple question
to ponder is whether a mapping class of S can be determined to be
pseudo-Anosov given only the data of its action on Gamma/Gamma_k for
some k. In this paper, to each mapping class f which acts trivially on
Gamma/Gamma_{k+1}, we associate an invariant Psi_k(f) in End(H_1(S,Z))
which is constructed from its action on Gamma/Gamma_{k+2}. We show that
if the characteristic polynomial of Psi_k(f) is irreducible over Z,
then f must be pseudo-Anosov. Some explicit mapping classes are then
shown to be pseudo-Anosov.


(13) Lens spaces obtainable by surgery on doubly primitive knots
by Kazuhiro Ichihara and Toshio Saito

In this paper, we consider which lens spaces are obtainable by Dehn
surgery described by Berge on doubly primitive knots. An algorithm
is given to decide whether a given lens space is obtainable by such a
surgery. Also included is a complete characterization of such surgeries
yielding lens spaces with Klein bottles.


(14) The homotopy infinite symmetric product represents stable homotopy
by Christian Schlichtkrull

We modify the definition of the infinite symmetric product of a based
space X by applying the homotopy colimit instead of the colimit. This
gives a topological monoid SP_h(X) and using formal properties of
homotopy colimits, we prove that its group completion represents the
stable homotopy of X. In this way we get a streamlined approach to the
Barratt-Priddy-Quillen theorem.


(15) Non-finiteness results for Nil-groups
by Joachim Grunewald

Generalizing an idea of Farrell we prove that for a ring Lambda and a
ring automorphism alpha of finite order the groups Nil_0(Lambda;alpha)
and all of its p-primary subgroups are either trivial or not finitely
generated as an abelian group. We also prove that if beta and gamma
are ring automorphisms such that beta o gamma is of finite order then
Nil_0(Lambda;Lambda_beta,Lambda_gamma) and all of its p-primary subgroups
are either trivial or not finitely generated as an abelian group. These
Nil-groups include the Nil-groups appearing in the decomposition of K_i
of virtually cyclic groups for i <= 1.


(16) On the virtual Betti numbers of arithmetic hyperbolic 3-manifolds
by D Cooper, D D Long and A W Reid

We show that if an arithmetic hyperbolic 3-manifold has virtual positive
Betti number, then it has virtual infinite Betti number. This has the
consequence that all such manifolds have large fundamental group.


(17) Knot Floer homology of Whitehead doubles
by Matthew Hedden

In this paper we study the knot Floer homology invariants of the
twisted and untwisted Whitehead doubles of an arbitrary knot K. We
present a formula for the filtered chain homotopy type of HFK(D(+,K,t))
in terms of the invariants for K, where D(+,K,t) denotes the t-twisted
positive-clasped Whitehead double of K. In particular the formula
can be used iteratively and can be used to compute the Floer homology
of manifolds obtained by surgery on Whitehead doubles. An immediate
corollary is that tau(D(+,K,t)) = 1 if t < 2tau(K) and zero otherwise,
where tau is the Ozsvath-Szabo concordance invariant. It follows
that the iterated untwisted Whitehead doubles of a knot satisfying
tau(K)>0 are not smoothly slice.


(18) On combinatorial link Floer homology
by Ciprian Manolescu, Peter Ozsvath, Zoltan Szabo and Dylan Thurston

Link Floer homology is an invariant for links defined using a suitable
version of Lagrangian Floer homology. In an earlier paper, this invariant
was given a combinatorial description with mod 2 coefficients. In
the present paper, we give a self-contained presentation of the basic
properties of link Floer homology, including an elementary proof of its
invariance. We also fix signs for the differentials, so that the theory
is defined with integer coefficients.


(19) Flexing closed hyperbolic manifolds.
by D Cooper, D D Long and M B Thistlethwaite

We show that for certain closed hyperbolic manifolds, one can nontrivially
deform the real hyperbolic structure when it is considered as a real
projective structure. It is also shown that in the presence of a mild
smoothness hypothesis, the existence of such real projective deformations
is equivalent to the question of whether one can nontrivially deform
the canonical representation of the real hyperbolic structure when it
is considered as a group of complex hyperbolic isometries. The set of
closed hyperbolic manifolds for which one can do this seems mysterious.

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