Factorability, discrete morse theory and a reformulation of K(π, 1)-conjecture

Ozornova, Viktoriya

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Thesis

Factorability, discrete morse theory and a reformulation of K(π, 1)-conjecture

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Ozornova, Viktoriya
Max Planck Institute for Mathematics, Max Planck Society;

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https://hdl.handle.net/20.500.11811/5621
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Citation

Ozornova, V. (2013). Factorability, discrete morse theory and a reformulation of K(π, 1)-conjecture. PhD Thesis, Rheinische Friedrich-Wilhelm-Universität, Bonn.

Cite as: https://hdl.handle.net/21.11116/0000-0004-18BA-0

Abstract

The first aim of this thesis is to study factorable groups and monoids. We give a new family of examples for factorability structures, provided by Garside theory, in particular, we provide a factorability structure on braid groups. Furthermore, we investigate the connection between factorability structures and rewriting systems, and give conditions under which a factorability structure yields a complete rewriting system on a monoid. Moreover, we exhibit a factorability structure on the orthogonal group O(n) and the induced factorability structure on the reflection subgroup of type B(n).
Another aim of this thesis is the study of Artin groups and monoids. We exhibit several chain complexes computing the homology of an Artin monoid. Moreover, we give a new proof for Dobrinskaya's Theorem which states a reformulation of the K(π,1)-conjecture for Artin groups.