Event calendar file
School of Mathematics Colloquium
A finite combinatorial presentation for closed smooth manifolds
by Prof. L.C. Siebenmann (U. Paris-Sud, Orsay, France)
Wednesday, July 10, 2013
from
to
(Asia/Kolkata)
at Colaba Campus ( AG-69 )
at Colaba Campus ( AG-69 )
| Description |
I will define a class of finite simplicial n-complexes K simplexwise linearly embedded in \R^{n+s} such that, by a well defined smoothing process, K inherits from \R^{n+s} a smooth submanifold structure that is well defined up to concordance in the sense of M. Hirsch. Every
closed smooth n-submanifold of \R^{n+s} is so presented. Ideas of S.Cairns and J.H.C. Whitehead are used.
In 1991, Macpherson conjectured a quite different finite combinatorial presentation for closed smooth manifolds; it involves matroids. But the
basic question whether it really determines a smooth structure up to diffeomorphism or concordance is (I believe) still open.
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