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Branched Spines approach to combinatorial Heegaard Floer homology
by
Carl Hammarsten
George Washington University
A 3-dimensional closed manifold Y represented by its branched spine has a canonical Heegaard decomposition. We present this decomposition graphically in the form of a Strip Diagram. We then show that strip diagrams have nice properties which greatly simplify the calculation of Heegaard Floer homology. Motivated by this work, we present a combinatorial definition of a chain complex which we expect to be homotopically equivalent to the Heegaard Floer one, yet significantly smaller. Finally, we consider the presentation of a branched spine by its O-graph and show how to reformulate our definition in these terms.
Date received: May 7, 2014
Copyright © 2014 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 # cbjb-11.