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GENERA AND DEGREES OF TORUS KNOTS IN ℂP²

MOHAMED AIT NOUH

Department of Mathematics, University of California at Riverside, 900 University Avenue, Riverside, CA 92521, USA

https://doi.org/10.1142/S0218216509007439Cited by:7 (Source: Crossref)

Abstract

The ℂP²-genus of a knot K is the minimal genus over all isotopy classes of smooth, compact, connected and oriented surfaces properly embedded in ℂP² - B⁴ with boundary K. We compute the ℂP²-genus and realizable degrees of (-2,q)-torus knots for 3 ≤ q ≤ 11 and (2,q)-torus knots for 3 ≤ q ≤ 17. The proofs use gauge theory and twisting operations on knots.

Keywords:

AMSC: 57M25, 57M27

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