Trivial Cocycles and Invariants of Homology 3-Spheres

2006/05/29 by Wolfgang Pitsch, Pitsch, Wolfgang · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #math.GT #math.KT #msc:20J05 #msc:57M27

paper · pdf · doi:10.48550/arxiv.math/0605725

25 pages, 12 figures

arxiv created 2006/05/29 · arxiv updated 2009/12/01

Abstract

We study the relationship between trivial cocycles on the Torelli group and invariants of oriented integral homology 3-spheres. We give ncecessary and sufficient conditions for a function defined on the union of the Torelli groups to be an invariant of homology spheres. We apply this study to give a new purely algebraic construction of the Casson invariant and prove in this setting its surgery properties. As a by-product we get a new 2-torsion cohomology class in the second integral cohomology of the Torelli group.

Citations

• Die Gruppe der Abbildungsklassen: Das arithmetische Feld auf Flächen

Cited by

• A Parametrization of Integral Homology 3-Spheres by the Fourth Johnson subgroup

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