Integral homology -spheres and the Johnson filtration
Author:
Wolfgang Pitsch
Journal:
Trans. Amer. Math. Soc. 360 (2008), 2825-2847
MSC (2000):
Primary 57M99; Secondary 20F38, 20F12
DOI:
https://doi.org/10.1090/S0002-9947-08-04208-6
Published electronically:
January 4, 2008
MathSciNet review:
2379777
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: The mapping class group of an oriented surface of genus
with one boundary component has a natural decreasing filtration
, where
is the kernel of the action of
on the
nilpotent quotient of
. Using a tree Lie algebra approximating the graded Lie algebra
we prove that any integral homology sphere of dimension
has for some
a Heegaard decomposition of the form
, where
and
is such that
. This proves a conjecture due to S. Morita and shows that the ``core'' of the Casson invariant is indeed the Casson invariant.
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Additional Information
Wolfgang Pitsch
Affiliation:
Departament de Matemàtiques, Universitat Autònoma de Barcelona, E-08193 Bellaterra, Spain
Email:
pitsch@mat.uab.es
DOI:
https://doi.org/10.1090/S0002-9947-08-04208-6
Received by editor(s):
November 7, 2005
Published electronically:
January 4, 2008
Additional Notes:
The author was supported by MEC grant MTM2004-06686 and by the program Ramón y Cajal, MEC, Spain
Article copyright:
© Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.