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Graph complexes and their cohomology


Zivkovic, Marco. Graph complexes and their cohomology. 2016, University of Zurich, Faculty of Science.

Abstract

In this thesis we study cohomologies of two kind of graph complexes, Kontsevich graph complexes and hairy graph complexes, by three dfferent methods. In the first method we combinatorially calculate the dimensions of Kontsevich graph complexes by providing generating functions, leading to the Euler characteristics. Secondly, we prove that multiple edges may be omitted without essentially changing the cohomology in both type of complexes. The third method introduces extra dfferentials on all complexes, leading to spectral sequences that converge to (almost) zero with the standard dfferential being the first one. This leads to the conclusion that classes of standard cohomology come in pairs.

Abstract

In this thesis we study cohomologies of two kind of graph complexes, Kontsevich graph complexes and hairy graph complexes, by three dfferent methods. In the first method we combinatorially calculate the dimensions of Kontsevich graph complexes by providing generating functions, leading to the Euler characteristics. Secondly, we prove that multiple edges may be omitted without essentially changing the cohomology in both type of complexes. The third method introduces extra dfferentials on all complexes, leading to spectral sequences that converge to (almost) zero with the standard dfferential being the first one. This leads to the conclusion that classes of standard cohomology come in pairs.

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Additional indexing

Item Type:Dissertation (monographical)
Referees:Cattaneo Alberto S, Turchin Victor, Willwacher Thomas
Communities & Collections:07 Faculty of Science > Institute of Mathematics
UZH Dissertations
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2016
Deposited On:27 Oct 2016 10:39
Last Modified:15 Apr 2021 14:36
Number of Pages:101
OA Status:Green

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