Towards invariants of surfaces in 4-space via classical link invariants

Lee, Sang

doi:10.1090/S0002-9947-08-04568-6

Towards invariants of surfaces in $4$-space via classical link invariants
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by Sang Youl Lee PDF

Trans. Amer. Math. Soc. 361 (2009), 237-265 Request permission

Abstract:

In this paper, we introduce a method to construct ambient isotopy invariants for smooth imbeddings of closed surfaces into $4$-space by using hyperbolic splittings of the imbedded surfaces and an arbitrary given isotopy or regular isotopy invariant of classical knots and links in $3$-space. Using this construction, adopting the Kauffman bracket polynomial as an example, we produce some invariants.

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