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Strip Diagram 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 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 have proven is 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 that reformulating our definition in these terms gives a clock-state type description for HF-hat of Y.
Date received: December 1, 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 # cbjz-20.