A formula for the action of Dehn twists on HOMFLY-PT skein modules and its applications
Tsuji, Shunsuke
Original · EN
We introduce a formula for the action of Dehn twists on the HOMFLY-PT type skein module of a surface. As an application of the formula to mapping class group, we give an embedding from the Torelli group of a surface Σg,₁ of genus g with non-empty connected boundary into the completed HOMFLY-PT type skein algebra. As an application of the formula to integral homology 3-spheres, we construct an invariant z(M) ∈ Q [ρ] [[h]] for an integral homology 3-sphere M. The invariant z(M) (hⁿ⁺¹) is a finite type invariant of order n.
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