Seifert circles,braid index and the algebraic crossing number |
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Affiliation: | 1. Institute of Mathematics, Physics and Mechanics, University of Ljubljana, PO Box 2964, 1000 Ljubljana, Slovenia;2. Department of Mathematics, Warsaw University, ul. Banacha 2, 02-097 Warsaw, Poland |
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Abstract: | We introduce new operations reducing the number of Seifert circles in link diagrams of a special type. The operations are similar to one described in [Mem. Amer. Math. Soc. 508 (1993)] and [Math. Proc. Cambridge Philos. Soc. 111 (2) (1992) 273]. We discuss a conjecture about the number of Seifert circles that can be canceled by applying the operation repeatedly. We translate the problem into one belonging to graph theory. |
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