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Heegaard Floer Homology
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| Organizers |
Prof. Norbert A'Campo (Basel) Prof. Anna Beliakova (Uni Zurich) Dr. Alexandru Oancea (ETHZ) Prof. Dietmar Salamon (ETHZ) Stephan Wehrli (Basel) |
| Location | HG E 33.5 |
| Time | Wednesday 16:15-18:00 or 17:15-19:00 (to be confirmed) |
| Starts on | October 20, 2004 |
| Contact |
Alexandru Oancea (oancea@math.ethz.ch) http://www.math.ethz.ch/~oancea/ |
| Description |
Peter Ozsvath and Zoltan Szabo recently constructed a Floer homology theory leading to invariants of 3-manifolds and knots. They exploit the existence of Heegaard decompositions, i.e. the possibility to write any 3-manifold as a union of two handlebodies glued along their common boundary, in order to give a geometric counterpart of Seiberg-Witten theory. Although the precise relationship between these theories is still unknown, the main applications of Seiberg-Witten invariants were indeed reproduced in the Ozsvath-Szabo setting. The aim of our seminar is to understand the Ozsvath-Szabo construction. We intend to give a comprehensive introduction to its main building blocks: Lagrangian Floer homology and Gromov's theory of pseudo-holomorphic disks. A further seminar devoted to applications of Ozsvath and Szabo's theory to low dimensional topology and, in particular, to its relationship with Khovanov homology is planned for SS05. Diploma-, Master- and Ph.D. students interested in modern developments of low dimensional topology and symplectic geometry are kindly invited to join our seminar. Basic knowledge in these fields would be an advantage. |
| References |
1. Ozsvath, P., Szabo, Z.: Holomorphic disks and topological invariants for closed three-manifolds, to appear in Annals of Math., arXiv: math.SG/0101206 2. Ozsvath, P., Szabo, Z.: Holomorphic disks and three-manifold invariants: properties and applications, to appear in Annals of Math., arXiv:math.SG/0105202 3. (survey paper) Ozsvath, P., Szabo, Z.: Heegaard diagrams amd holomorphic disks, arXiv:math.SG/0403029 |
| Additional Information | See http://www.math.ethz.ch/~oancea/eng/heegaard.html for a list of the talks. |
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