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Kirby calculus for null-homotopic and null-homologous framed links in 3-manifolds


Widmer, Tamara Tajara. Kirby calculus for null-homotopic and null-homologous framed links in 3-manifolds. 2014, University of Zurich, Faculty of Science.

Abstract

A theorem of Kirby gives a necessary and sufficient condition for two framed links in S3 to yield orientation-preserving diffeomorphic results of surgery. Kirby's theorem is an important method for constructing invariants of 3-manifolds. In this paper, we prove a variant of Kirby's theorem for null-homologous framed links in a 3-manifold. This result involves a new kind of moves, called IHX-moves, which are closely related to the IHX relation in the theory of finite type invariants. When the first homology group of M is free abelian, we give a refinement of this result to ±1-framed, algebraically split, null-homologous framed links in M.

Abstract

A theorem of Kirby gives a necessary and sufficient condition for two framed links in S3 to yield orientation-preserving diffeomorphic results of surgery. Kirby's theorem is an important method for constructing invariants of 3-manifolds. In this paper, we prove a variant of Kirby's theorem for null-homologous framed links in a 3-manifold. This result involves a new kind of moves, called IHX-moves, which are closely related to the IHX relation in the theory of finite type invariants. When the first homology group of M is free abelian, we give a refinement of this result to ±1-framed, algebraically split, null-homologous framed links in M.

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Item Type:Dissertation (monographical)
Referees:Beliakova Anna
Communities & Collections:UZH Dissertations
Dewey Decimal Classification:Unspecified
Language:English
Place of Publication:Zürich
Date:2014
Deposited On:27 Mar 2019 14:01
Last Modified:07 Apr 2020 07:17
Number of Pages:135
OA Status:Green
Related URLs:https://www.recherche-portal.ch/primo-explore/fulldisplay?docid=ebi01_prod010162097&context=L&vid=ZAD&search_scope=default_scope&tab=default_tab&lang=de_DE (Library Catalogue)

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