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

Access to Document

10.1016/j.aim.2008.09.002

Link to publication in Scopus

Fingerprint Dive into the research topics of 'Trivial cocycles and invariants of homology 3-spheres'. Together they form a unique fingerprint.

Cite this

@article{e8df1512fc684ceba8790d2d1f7ef5b3,

title = "Trivial cocycles and invariants of homology 3-spheres",

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.",

year = "2009",

month = jan,

day = "15",

doi = "10.1016/j.aim.2008.09.002",

language = "Ingl{\'e}s estadounidense",

volume = "220",

pages = "278--302",

journal = "Advances in Mathematics",

issn = "0001-8708",

publisher = "Academic Press Inc.",

number = "1",

}

TY - JOUR

T1 - Trivial cocycles and invariants of homology 3-spheres

AU - Pitsch, Wolfgang

N1 - Funding Information: E-mail address: pitsch@mat.uab.es. 1 The author is supported by MEC grant MTM2004-06686 and by the program Ramón y Cajal, MEC, Spain. Copyright: Copyright 2008 Elsevier B.V., All rights reserved.

PY - 2009/1/15

Y1 - 2009/1/15

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.

KW - Casson invariant

KW - Heegaard splitting

KW - Homology spheres

KW - Torelli group

UR - http://www.scopus.com/inward/record.url?scp=54449089407&partnerID=8YFLogxK

U2 - 10.1016/j.aim.2008.09.002

DO - 10.1016/j.aim.2008.09.002

M3 - Artículo

AN - SCOPUS:54449089407

VL - 220

SP - 278

EP - 302

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

IS - 1

ER -