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L²-homology and reciprocity for right-angled Coxeter groups

Boris Okun, Richard Scott (2011)

Fundamenta Mathematicae

Let W be a Coxeter group and let μ be an inner product on the group algebra ℝW. We say that μ is admissible if it satisfies the axioms for a Hilbert algebra structure. Any such inner product gives rise to a von Neumann algebra μ containing ℝW. Using these algebras and the corresponding von Neumann dimensions we define L ² μ -Betti numbers and an L ² μ -Euler charactersitic for W. We show that if the Davis complex for W is a generalized homology manifold, then these Betti numbers satisfy a version of Poincaré...

Legendrian and transverse twist knots

John B. Etnyre, Lenhard L. Ng, Vera Vértesi (2013)

Journal of the European Mathematical Society

In 1997, Chekanov gave the first example of a Legendrian nonsimple knot type: the m ( 5 2 ) knot. Epstein, Fuchs, and Meyer extended his result by showing that there are at least n different Legendrian representatives with maximal Thurston-Bennequin number of the twist knot K - 2 n with crossing number 2 n + 1 . In this paper we give a complete classification of Legendrian and transverse representatives of twist knots. In particular, we show that K - 2 n has exactly n 2 2 Legendrian representatives with maximal Thurston–Bennequin...

Legendrian graphs and quasipositive diagrams

Sebastian Baader, Masaharu Ishikawa (2009)

Annales de la faculté des sciences de Toulouse Mathématiques

In this paper we clarify the relationship between ribbon surfaces of Legendrian graphs and quasipositive diagrams by using certain fence diagrams. As an application, we give an alternative proof of a theorem concerning a relationship between quasipositive fiber surfaces and contact structures on S 3 . We also answer a question of L. Rudolph concerning moves of quasipositive diagrams.

Les invariants θ p des 3-variétés périodiques

Nafaa Chbili (2001)

Annales de l’institut Fourier

Soit r un entier > 1 . Une 3-variété M est dite r -périodique si et seulement si le groupe cyclique G = / r agit semi-librement sur M avec un cercle comme l’ensemble des points fixes. Dans cet article, nous utilisons les invariants quantiques θ p pour établir des conditions nécessaires pour qu’une 3-variété soit périodique.

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