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On a monoid associated to knotted surfaces in special form
by
Michal Jablonowski
University of Gdansk
We introduce monoid corresponding to knotted surfaces in four sphere and present over a dozen relations among its four type of generators. Then we wish to investigate an index associated to the monoid also being invariant for knotted surface. Using our relations we will briefly prove that there are exactly six types of surfaces with index less or equal to two, and there are infinitely many types of knotted surfaces with index equal to three. Also as a straightforward application we will show different proof of well known theorem about twist-spun knots.
Date received: November 21, 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-32.