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What and Who

Cobordism ring and genera

Zi Ye
Max-Planck-Institut für Informatik - D1
AG1 Mittagsseminar (own work)
AG 1, AG 2, AG 3, AG 4, AG 5, RG1, SWS, MMCI  
AG Audience
English

Date, Time and Location

Thursday, 8 May 2014
13:00
30 Minutes
E1 4
022
Saarbrücken

Abstract

Generally there are huge number of manifolds up to homeomorphism and it’s hard to classify them in high dimension. Cobordism class is a coarse classifica- tion of manifolds. Two n-dimensional manifolds whose disjoint union forms the boundary of a (n+1)-dimensional manifolds should be regarded as equivalent in the cobordism class. In this talk we are mainly concerned with the oriented cobordism ΩSO . First we study the examples of lower dimension, to find the generators of ΩSO . Since the direct observation becomes much more difficult as the dimension increased, we introduce the Pontryagin-Thom construction to give a precise description of the algebra structure of ΩSO of all dimensions.

Genera are ring homomorphisms from Ω∗ to Q. Here L-genus and Aˆ-genus are of great interest. After the definition of these genera we would briefly talk
about some of their applications, such as Hirzebruch signature theorem and the relation between positive scalar curvature and Aˆ-genus.

Contact

Natalia Klein
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Natalia Klein, 05/06/2014 13:13
Natalia Klein, 04/28/2014 09:23
Natalia Klein, 04/24/2014 11:55
Natalia Klein, 04/24/2014 11:53 -- Created document.