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Towards one conjecture on collapsing of the Serre spectral sequence

Markl, Martin (1990)

Proceedings of the Winter School "Geometry and Physics"

[For the entire collection see Zbl 0699.00032.] A fibration F E B is called totally noncohomologuous to zero (TNCZ) with respect to the coefficient field k, if H * ( E ; k ) H * ( F ; k ) is surjective. This is equivalent to saying that π 1 ( B ) acts trivially on H * ( F ; k ) and the Serre spectral sequence collapses at E 2 . S. Halperin conjectured that for c h a r ( k ) = 0 and F a 1-connected rationally elliptic space (i.e., both H * ( F ; 𝒬 ) and π * ( F ) 𝒬 are finite dimensional) such that H * ( F ; k ) vanishes in odd degrees, every fibration F E B is TNCZ. The author proves this being the case...

Trace functions on Iwahori-Hecke algebras

Meinolf Geck (1998)

Banach Center Publications

This paper is an expanded version of a talk given at the Banach Center Symposium on Knot Theory in July/August 1995. Its aim is to provide a general survey about trace functions on Iwahori-Hecke algebras associated with finite Coxeter groups. The so-called Markov traces are relevant to knot theory as they can be used to construct invariants of oriented knots and links. We present a classification of Markov traces for the classical types A, B and D.

Traces, lengths, axes and commensurability

Alan W. Reid (2014)

Annales de la faculté des sciences de Toulouse Mathématiques

The focus of this paper are questions related to how various geometric and analytical properties of hyperbolic 3-manifolds determine the commensurability class of such manifolds. The paper is for the large part a survey of recent work.

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