The Library
The parity of the Cochran--Harvey invariants of 3--manifolds
Tools
Friedl, Stefan and Kim, Taehee (2008) The parity of the Cochran--Harvey invariants of 3--manifolds. Transactions of the American Mathematical Society, Vol.360 (No.6). pp. 2909-2923. doi:10.1090/S0002-9947-08-04253-0 ISSN 0002-9947.
Research output not available from this repository.
Request-a-Copy directly from author or use local Library Get it For Me service.
Official URL: http://dx.doi.org/10.1090/S0002-9947-08-04253-0
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 higher-order 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 3-manifold 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 3-manifold 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 Cochran-Harvey invariant agrees with the parity of the Thurston norm.
Item Type: | Journal Article | ||||
---|---|---|---|---|---|
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Transactions of the American Mathematical Society | ||||
Publisher: | American Mathematical Society | ||||
ISSN: | 0002-9947 | ||||
Official Date: | 2008 | ||||
Dates: |
|
||||
Volume: | Vol.360 | ||||
Number: | No.6 | ||||
Page Range: | pp. 2909-2923 | ||||
DOI: | 10.1090/S0002-9947-08-04253-0 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
Request changes or add full text files to a record
Repository staff actions (login required)
View Item |