Trivial cocycles and invariants of homology 3-spheres

被引：5

作者：

Pitsch, Wolfgang ^{[1
]}

机构：

[1] Univ Autonoma Barcelona, Dept Matemat, E-08193 Bellaterra, Spain

来源：

ADVANCES IN MATHEMATICS | 2009年 / 220卷 / 01期

关键词：

Torelli group; Casson invariant; Heegaard splitting; Homology spheres; 3-DIMENSIONAL HANDLEBODY; CASSON INVARIANT; SURFACE BUNDLES; TORELLI GROUP; HOMEOMORPHISMS;

D O I：

10.1016/j.aim.2008.09.002

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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. (c) 2008 Elsevier Inc. All rights reserved.

引用

页码：278 / 302

页数：25

共 50 条

[41] AN INFINITE CLASS OF IRREDUCIBLE HOMOLOGY 3-SPHERES
GROSS, JL
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1970, 25 (01) : 173 - &
[42] On finite groups acting on homology 3-spheres
Reni, M
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2001, 63 : 226 - 246
[43] Automorphic forms and rational homology 3-spheres
Calegari, F
Dunfield, NM
GEOMETRY & TOPOLOGY, 2006, 10 : 295 - 329
[44] AN INFINITE CLASS OF IRREDUCIBLE HOMOLOGY 3-SPHERES
GROSS, JL
NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1970, 17 (02): : 403 - &
[45] CASSON INVARIANT OF SEIFERT HOMOLOGY 3-SPHERES
FUKUHARA, S
MATSUMOTO, Y
SAKAMOTO, K
MATHEMATISCHE ANNALEN, 1990, 287 (02) : 275 - 285
[46] A POLYNOMIAL INVARIANT OF INTEGRAL HOMOLOGY 3-SPHERES
OHTSUKI, T
MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1995, 117 : 83 - 112
[47] A polynomial invariant of rational homology 3-spheres
Ohtsuki, T
INVENTIONES MATHEMATICAE, 1996, 123 (02) : 241 - 257
[48] SLICING DOUBLES OF KNOTS IN HOMOLOGY 3-SPHERES
LITHERLAND, RA
INVENTIONES MATHEMATICAE, 1979, 54 (01) : 69 - 74
[49] Integral homology 3-spheres and the Johnson filtration
Pitsch, Wolfgang
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2008, 360 (06) : 2825 - 2847
[50] SEQUENCE OF HOMOLOGY 3-SPHERES - PRELIMINARY REPORT
DIBNER, S
NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1975, 22 (06): : A667 - A667

← 1 2 3 4 5 →