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Organizers |
Complexity of Virtual Multistrings
by
David Freund
Dartmouth College
A virtual n-string α is a collection of n closed curves on an oriented surface M. Associated to α, there are two natural measures of complexity: the genus of M and the number of intersection points. By considering virtual n-strings up to equivalence by virtual homotopy, i.e., homotopies of the component curves and stabilizations/destabilizations of the surface, a natural question is whether these quantities can be minimized simultaneously. We show that this is possible for non-parallel virtual n-strings and that, moreover, such a representative can be obtained by monotonically decreasing genus and the number of intersections from any initial representative.
Date received: October 19, 2017
Copyright © 2017 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 # cboj-06.