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Topology and commutativity of diagrams
by
Paul C. Kainen
Georgetown University
Robustness and iterative robustness of cycle bases are defined. The proof that some graphs cannot have a robust basis is given in the next talk by Richard Hammack, with whom this work is joint. We show that diagrams commute iff they are commutative when restricted to an iteratively robust basis of the underlying graph of the diagram. Theorem. Every graph has an iteratively robust basis. A non-commutative diagram is exhibited whose underlying graph has a cycle basis with all members commutative. So iterative robustness of the basis matters for the control of commutativity.
Date received: April 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 # cbof-18.