New link invariants and Polynomials (I), oriented case

Details New link invariants and Polynomials (I), oriented case New link invariants and Polynomials (I), oriented case

2010-04-13

arxiv.org/abs/1004.2085v4

Mathematics

Geometric Topology

15 figures, 37 pages

Scientific paper

Given any oriented link diagram, two types of new knot invariants are constructed. They satisfy some generalized skein relations. The coefficients of each invariant is from a commutative ring. Homomorphisms and representations of those rings define new link invariants. For example, the HOMFLYPT polynomial with three variables. In this sense, type one invariant is a generalization of the HOMFLYPT polynomial. Those invariants can also be modified by writhe and parameterized to get more powerful invariants. For example, the modified type one invariant distinguishes mutants, and the parameterized invariants produces information for crossing number.

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