Re: kung fu mereotopology

On Dec 21, 7:44 pm, Mariano Suárez-Alvarez
<mariano.suarezalva...@xxxxxxxxx> wrote:
On Dec 22, 1:01 am, galathaea <galath...@xxxxxxxxx> wrote:

i find that kontsevich is still working on his own much
and has a number of "huge" possibilities lurking

much of his stuff on operads
and graph theory
and combinatorial topology
is building some very powerful algebraic tools
which could potentially crack p = np among other big questions

Can you point to a sentence of Kontsevich related to
P = NP?

sure
but i wasn't claiming his actually mentioning such

i was thinking of
the algebraic approach to computational complexity

things like
http://www.math.ntu.edu.tw/talkdata/194/March10.ppt

and from the development of operad theory
i've seen much of that computational theory
transform to the algebraic language

particularly the theory of props in rewriting theory
has quite some start in such a formalisation

http://sigfpe.blogspot.com/2008/10/operads-and-their-monads.html

http://blog.mikael.johanssons.org/archive/2008/02/props-and-patches/

http://www.atlantis-press.com/php/download_paper.php?id=370

and particularly
the homological theory in computational complexity

kontsevich has been skirting algorithmic complexity
for some time now with his work on algebraic structures
over graphs and related combinatorial structures

probably the most suspicious to me is his
(loosely)

H (lie algebra) = H (graph complex) = H (group)
* * *

because the homology of graph complexes
has some immediate consequences
for graph isomorphism and the complexity of such algorithms

i have strong suspicions
that much of the operad theory on which this is built
(cf. http://arxiv.org/pdf/math/0211464)
contains the kernel of the algebraic concepts
that could crack complexity questions like p =?= np

additionally
there is known complexity work
on poset homology
that ties their algebraics to more classical work on matroids
http://www.springerlink.com/content/y60n827057m374n8/

kontsevich has contributed quite a bit to matroid theory
and generally has been working in that netherworld
of the algebraics of discrete combinatorial structures
with all the complexity issues just over the horizon

anyway
my point was that kontsevich has done some major work
and there is the potential
for resolving some very big questions

p =?= np is just one example from many
touched on by his work

like connes' attempts at RH
it's all conjectured relationships until something is proven

-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
galathaea: prankster, fablist, magician, liar
.