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We define the singular Hecke algebra $ℋ (S B_{n})$ as the quotient of the singular braid monoid algebra $ℂ (q) [S B_{n}]$ by the Hecke relations $σ_{k}^{2} = (q - 1) σ_{k} + q$ , $1 \leq k \leq n - 1$ . We define the notion of Markov trace in this context, fixing the number $d$ of singular points, and we prove that a Markov trace determines an invariant on the links with $d$ singular points which satisfies some skein relation. Let ${TR}_{d}$ denote the set of Markov traces with $d$ singular points. This is a $ℂ (q, z)$ -vector space. Our main result is that ${TR}_{d}$ is of dimension $d + 1$ . This result is completed...

Singular Lefschetz pencils.

Auroux, Denis, Donaldson, Simon K., Katzarkov, Ludmil (2005)

Geometry & Topology

Singularities and exotic spheres

Friedrich Hirzebruch (1966/1968)

Séminaire Bourbaki

Skein algebra of a group

Józef Przytycki, Adam Sikora (1998)

Banach Center Publications

We define for each group G the skein algebra of G. We show how it is related to the Kauffman bracket skein modules. We prove that skein algebras of abelian groups are isomorphic to symmetric subalgebras of corresponding group rings. Moreover, we show that, for any abelian group G, homomorphisms from the skein algebra of G to C correspond exactly to traces of SL(2,C)-representations of G. We also solve, for abelian groups, the conjecture of Bullock on SL(2,C) character varieties of groups - we show...

Skein algebras of the solid torus and symmetric spatial graphs

Nafaa Chbili (2006)

Fundamenta Mathematicae

We use the topological invariant of spatial graphs introduced by S. Yamada to find necessary conditions for a spatial graph to be periodic with a prime period. The proof of the main result is based on computing the Yamada skein algebra of the solid torus and then proving that it injects into the Kauffman bracket skein algebra of the solid torus.