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INVARIANTS OF SURFACE LINKS IN ℝ⁴ VIA SKEIN RELATION

SANG YOUL LEE

Department of Mathematics, Pusan National University, Pusan 609-735, Korea

https://doi.org/10.1142/S0218216508006221Cited by:6 (Source: Crossref)

Abstract

Using Yoshikawa's surface diagram, we constructed new invariants of ambient isotopy classes of smoothly embedded closed surfaces in ℝ⁴ via a state-sum model similar to the Kauffman's state-sum model for the Jones polynomial for classical knots and links in ℝ³. It is shown that the invariants can also be defined by skein relation and thus they are calculated from Yoshikawa's surface diagrams recurrently. Some of the properties of the invariants are given and explicit computations for several surfaces are included.

Keywords:

AMSC: 57Q45, 57M25

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