6533b85efe1ef96bd12bfede
RESEARCH PRODUCT
HOMFLY-PT skein module of singular links in the three-sphere
Emmanuel WagnerLuis Parissubject
[ MATH.MATH-GT ] Mathematics [math]/Geometric Topology [math.GT]HOMFFLY-PT skein modulePure mathematics01 natural scienceslaw.inventionMathematics - Geometric TopologylawMathematics::Quantum Algebra[MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT]0103 physical sciencessingular knot singular linkFOS: Mathematics0101 mathematicsQuotientMathematicsRing (mathematics)Algebra and Number TheorySkein010102 general mathematicsSkein relationGeometric Topology (math.GT)Mathematics::Geometric TopologyInvertible matrix57M25Isotopy010307 mathematical physicsdescription
For a ring R, we denote by [Formula: see text] the free R-module spanned by the isotopy classes of singular links in 𝕊3. Given two invertible elements x, t ∈ R, the HOMFLY-PT skein module of singular links in 𝕊3 (relative to the triple (R, t, x)) is the quotient of [Formula: see text] by local relations, called skein relations, that involve t and x. We compute the HOMFLY-PT skein module of singular links for any R such that (t-1 - t + x) and (t-1 - t - x) are invertible. In particular, we deduce the Conway skein module of singular links.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2012-06-11 |