English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Given a finitely presented group G and an epimorphism G to the group ofintegers Cochran and Harvey defined a sequence of integral invariants, whichcan be viewed as the degrees of higher--order Alexander polynomials. Cochranand Harvey showed that (up to a minor modification) this is a never decreasingsequence of numbers if G is the fundamental group of a 3-manifold with empty ortoroidal boundary, and that these invariants give lower bounds on the Thurstonnorm.  Using a certain Cohn localization and the duality of Reidemeister torsion weshow that for a fundamental group of a 3--manifold any jump in the sequence isnecessarily even. This answers in particular a question of Cochran. Furthermoreusing results of Turaev we show that under a mild extra hypothesis the parityof the Cochran--Harvey invariant agrees with the parity of the Thurston norm.

The parity of the Cochran--Harvey invariants of 3--manifolds