Trivial cocycles and invariants of homology 3-spheres

Wolfgang Pitsch

doi:10.1016/j.aim.2008.09.002

Trivial cocycles and invariants of homology 3-spheres

Wolfgang Pitsch^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

1 Citation (Scopus)

Abstract

We study the relationship between trivial cocycles on the Torelli group and invariants of oriented integral homology 3-spheres. We apply this study to give a new purely algebraic construction of the Casson invariant. As a by-product we get a new 2-torsion cohomology class in the second integral cohomology of the Torelli group.

Original language	American English
Pages (from-to)	278-302
Number of pages	25
Journal	Advances in Mathematics
Volume	220
Issue number	1
DOIs	https://doi.org/10.1016/j.aim.2008.09.002
Publication status	Published - 15 Jan 2009

Keywords

Casson invariant
Heegaard splitting
Homology spheres
Torelli group

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10.1016/j.aim.2008.09.002

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abstract = "We study the relationship between trivial cocycles on the Torelli group and invariants of oriented integral homology 3-spheres. We apply this study to give a new purely algebraic construction of the Casson invariant. As a by-product we get a new 2-torsion cohomology class in the second integral cohomology of the Torelli group.",

keywords = "Casson invariant, Heegaard splitting, Homology spheres, Torelli group",

author = "Wolfgang Pitsch",

note = "Funding Information: E-mail address: pitsch@mat.uab.es. 1 The author is supported by MEC grant MTM2004-06686 and by the program Ram{\'o}n y Cajal, MEC, Spain. Copyright: Copyright 2008 Elsevier B.V., All rights reserved.",

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N2 - We study the relationship between trivial cocycles on the Torelli group and invariants of oriented integral homology 3-spheres. We apply this study to give a new purely algebraic construction of the Casson invariant. As a by-product we get a new 2-torsion cohomology class in the second integral cohomology of the Torelli group.

AB - We study the relationship between trivial cocycles on the Torelli group and invariants of oriented integral homology 3-spheres. We apply this study to give a new purely algebraic construction of the Casson invariant. As a by-product we get a new 2-torsion cohomology class in the second integral cohomology of the Torelli group.

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KW - Heegaard splitting

KW - Homology spheres

KW - Torelli group

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Trivial cocycles and invariants of homology 3-spheres

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Keywords

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