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Simple ribbon fusions and genera of links
by
Tatsuya Tsukamoto
Osaka Institute of Technology
Coauthors: Kengo Kishimoto, Tetsuo Shibuya
Gabai and Scharlemann showed the superadditivity of genera of knots under a band sum, and that equality holds if and only if the band sum is just a connected sum.
However when we extend the theorem to links, we have a problem for the equality.
In fact, there is a band sum of a link L and the trivial 2-component link which produces a link L' such that the genus of L' is equal to the genus of L, but L' is not ambient isotopic to L (This fusion is realized by a simple ribbon fusion, which we introduce in the talk). However Goldberg's 2nd genera of L is not equal to that of L'. In this talk, we talk about the superadditivity of Goldberg's v-th genera of links under simple ribbon fusions.
Date received: November 13, 2012
Copyright © 2012 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cbfw-21.