Trivial cocycles and invariants of homology 3-spheres
| Autor: | Wolfgang Pitsch |
|---|---|
| Rok vydání: | 2009 |
| Předmět: |
Pure mathematics
Mathematics(all) General Mathematics 57M27 (Primary) Homology (mathematics) Torelli group Casson invariant Mathematics::Algebraic Topology Heegaard splitting Mathematics - Geometric Topology Mathematics::K-Theory and Homology FOS: Mathematics Mathematics 20J05 (Secondary) Factor system Geometric Topology (math.GT) K-Theory and Homology (math.KT) Algebraic construction Mathematics::Geometric Topology Cohomology Torelli theorem Algebra Mayer–Vietoris sequence Homology spheres Mathematics - K-Theory and Homology SPHERES |
| Zdroj: | Advances in Mathematics. 220(1):278-302 |
| ISSN: | 0001-8708 |
| DOI: | 10.1016/j.aim.2008.09.002 |
| Popis: | 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. Comment: 25 pages, 12 figures |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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