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Constructing Seifert surfaces from n-bridge link projections
Geometry/Topology| Speaker: | Joan Licata, Stanford University |
| Location: | 2112 MSB |
| Start time: | Wed, Apr 23 2008, 4:10PM |
The Thurston norm generalizes the notion of knot genus by considering the Euler characteristics of surfaces representing arbitrary relative second homology classes in a link complement. Ozsvath and Szabo showed that their Heegaard Floer link invariant (HFL-hat) detects the Thurston norm, but there is no systematic method for actually constructing a minimal-complexity surface representing a fixed homology class. In this talk I'll discuss an algorithm for constructing surfaces from n-bridge link projections. In the case of Seifert surfaces for alternating projections, this construction agrees with Seifert's algorithm and produces minimal complexity (Thurston norm-realizing) surfaces. However, I will also present examples of knots for which this algorithm constructs a surface realizing the knot genus when this is strictly less than the canonical genus.