Completion of publication of GT Monograph 16

Geometry & Topology Publications is pleased to announce completion
of the publication of GT Monograph Volume 16 (2009):

New Topological Contexts for Galois Theory and Algebraic Geometry
(BIRS 2008) edited by Andrew Baker and Birgit Richter


Five papers have been added:

(1) Geometry & Topology Monographs 16 (2009) 283-330
The construction of E_infty ring spaces from bipermutative categories
by J P May
URL: http://www.msp.warwick.ac.uk/gtm/2009/16/p010.xhtml
DOI: 10.2140/gtm.2009.16.283

(2) Geometry & Topology Monographs 16 (2009) 331-365
What are E_infty ring spaces good for?
by J P May
URL: http://www.msp.warwick.ac.uk/gtm/2009/16/p011.xhtml
DOI: 10.2140/gtm.2009.16.331

(3) Geometry & Topology Monographs 16 (2009) 367-400
Hopf Galois theory: A survey
by Susan Montgomery
URL: http://www.msp.warwick.ac.uk/gtm/2009/16/p012.xhtml
DOI: 10.2140/gtm.2009.16.367

(4) Geometry & Topology Monographs 16 (2009) 401-544
Topological logarithmic structures
by John Rognes
URL: http://www.msp.warwick.ac.uk/gtm/2009/16/p013.xhtml
DOI: 10.2140/gtm.2009.16.401

(5) Geometry & Topology Monographs 16 (2009) 545-592
The cyclotomic trace for symmetric ring spectra
by Christian Schlichtkrull
URL: http://www.msp.warwick.ac.uk/gtm/2009/16/p014.xhtml
DOI: 10.2140/gtm.2009.16.545

Abstracts follow

(1) The construction of E_infty ring spaces from bipermutative categories
by J P May

The construction of E_infty ring spaces and thus E_infty ring spectra
from bipermutative categories gives the most highly structured way of
obtaining the K-theory commutative ring spectra. The original
construction dates from around 1980 and has never been superseded, but
the original details are difficult, obscure, and slightly wrong. We
rework the construction in a much more elementary fashion.


(2) What are E_infty ring spaces good for?
by J P May

Infinite loop space theory, both additive and multiplicative, arose
largely from two basic motivations. One was to solve calculational
questions in geometric topology. The other was to better understand
algebraic K-theory. The Adams conjecture is intrinsic to the first
motivation, and Quillen's proof of that led directly to his original,
calculationally accessible, definition of algebraic K-theory. In
turn, the infinite loop understanding of algebraic K-theory feeds back
into the calculational questions in geometric topology. For example,
use of infinite loop space theory leads to a method for determining
the characteristic classes for topological bundles (at odd primes) in
terms of the cohomology of finite groups. We explain just a little
about how all that works, focusing on the central role played by
E_infty ring spaces.


(3) Hopf Galois theory: A survey
by Susan Montgomery

We consider a Hopf Galois extension B in A, for A a comodule algebra
over the Hopf algebra H with coinvariant algebra B. After giving a
number of examples, we discuss Galois extensions with additional
properties, such as having a normal basis. We then consider when there
is a category equivalence between the category of modules over B and
the category of "relative Hopf modules" for A and H. Finally we
discuss more recent work of van Oystaeyen and Zhang and of Schauenburg
on obtaining correspondence theorems between suitable subalgebras of A
and Hopf ideals of H.


(4) Topological logarithmic structures
by John Rognes

We develop a theory of logarithmic structures on structured ring spectra,
including constructions of logarithmic topological Andre-Quillen
homology and logarithmic topological Hochschild homology.


(5) The cyclotomic trace for symmetric ring spectra
by Christian Schlichtkrull

The purpose of this paper is to present a simple and explicit
construction of the Bokstedt-Hsiang-Madsen cyclotomic trace relating
algebraic K-theory and topological cyclic homology. Our construction
also incorporates Goodwillie's idea of a global cyclotomic trace.


.

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