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1995•Journal of Knot Theory and Its RamificationsRequires access

THE (2, ∞)-SKEIN MODULE OF THE COMPLEMENT OF A (2, 2p+1) TORUS KNOT

Doug Bullock

Open publisher page 46 citations

Abstract

In this paper we extend the list of three manifolds for which the (2, ∞)-skein module is known by giving the first explicit calculations for non-trivial knot exteriors. We show that for the complement of a (2, 2p+1) torus knot the module is free with a very simple basis. As a consequence, we obtain a family of polynomial invariants for links in these manifolds. The invariants are analogous to the Jones polynomial for links in S3.

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What this paper is about

In this paper we extend the list of three manifolds for which the (2, ∞)-skein module is known by giving the first explicit calculations for non-trivial knot exteriors. We show that for the complement of a (2, 2p+1) torus knot the module is free with a very simple basis. As a consequence, we obtain a family of polynomial invariants for links in these manifolds. The invariants are analogous to the Jones polynomial for links in S3.

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Available abstract

In this paper we extend the list of three manifolds for which the (2, ∞)-skein module is known by giving the first explicit calculations for non-trivial knot exteriors. We show that for the complement of a (2, 2p+1) torus knot the module is free with a very simple basis. As a consequence, we obtain a family of polynomial invariants for links in these manifolds. The invariants are analogous to the Jones polynomial for links in S3.

Key concepts: Skein, Mathematics, Knot complement, Quantum invariant, Skein relation, Torus, Knot invariant, Knot theory

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