TUBE-EQUIVALANCE OF SPANNING SURFACES AND SEIFERT SURFACES

Author (s) : Dr.D.VIDHYA and Dr.D.ANITHADEVI

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Abstract :
In this paper, the tools familiar to the knot theorist, i.e., the Reidemeister moves, the Seifert algorithm, and cut and paste, Bar-Natan, Fulman, and Kauffman have proved that spanning surfaces are tube-equivalent for possibly disconnected spanning surfaces. Connectivity is added to the assumption and we show: If S₁ and S₂ are Seifert surfaces for the link L, then S₁ and S₂ are tube-equivalent. The proof proceeds by examining how changes to a projection of a link affect the corresponding Seifert surfaces. Maintaining connectedness of a surface allows for controlling the first homology and the Seifert pairing by S-equivalence, and thus, is used in proving that the Alexander polynomial of the given link is an invariant.

Keywords : Spanning surfaces, Seifert pairing

Conference Date : 30/08/2019

Pages : 161

Paper ID : 19159