The parity of the CochranHarvey invariants of 3manifolds
Authors:
Stefan Friedl and Taehee Kim
Journal:
Trans. Amer. Math. Soc. 360 (2008), 29092922
MSC (2000):
Primary 57M27; Secondary 57M05
Published electronically:
January 7, 2008
MathSciNet review:
2379780
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Abstract: Given a finitely presented group and an epimorphism Cochran and Harvey defined a sequence of invariants , which can be viewed as the degrees of higherorder Alexander polynomials. Cochran and Harvey showed that (up to a minor modification) this is a never decreasing sequence of numbers if is the fundamental group of a 3manifold with empty or toroidal boundary. Furthermore they showed that these invariants give lower bounds on the Thurston norm. Using a certain Cohn localization and the duality of Reidemeister torsion we show that for a fundamental group of a 3manifold any jump in the sequence is necessarily even. This answers in particular a question of Cochran. Furthermore using results of Turaev we show that under a mild extra hypothesis the parity of the CochranHarvey invariant agrees with the parity of the Thurston norm.
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Additional Information
Stefan Friedl
Affiliation:
Department of Mathematics, Rice University, Houston, Texas 770051892
Address at time of publication:
Département de Mathématiques, UQAM, C.P. 8888, Succursale Centreville, Montréal, Quebec, Canada H3C 3P8
Email:
friedl@math.rice.edu
Taehee Kim
Affiliation:
Department of Mathematics, Konkuk University, Hwayangdong, Gwangjingu, Seoul 143701, Korea
Email:
tkim@konkuk.ac.kr
DOI:
http://dx.doi.org/10.1090/S0002994708042530
PII:
S 00029947(08)042530
Keywords:
Thurston norm,
3manifold groups,
Alexander polynomials
Received by editor(s):
October 25, 2005
Received by editor(s) in revised form:
February 13, 2006
Published electronically:
January 7, 2008
Additional Notes:
The second author is the corresponding author for this paper
Article copyright:
© Copyright 2008
American Mathematical Society
