Trivial Cocycles and Invariants of Homology 3-Spheres

Details Trivial Cocycles and Invariants of Homology 3-Spheres Trivial Cocycles and Invariants of Homology 3-Spheres

2006-05-29

arxiv.org/abs/math/0605725v1

Mathematics

Geometric Topology

25 pages, 12 figures

Scientific paper

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.

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