Beliakova
Fakultäten » Mathematisch-naturwissenschaftliche Fakultät » Mathematik, Institut für » Reine Mathematik » Prof. Dr. Anna Beliakova » Beliakova
Current research project
| Title / Titel | Khovanov and Floer Homology | ||||
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| Abstract (PDF, 14 KB) | |||||
| Summary / Zusammenfassung | Recently Khovanov defined a chain complex associated to a knot, whose Euler characteristic is the Jones polynomial and whose Poincare polynomial is a new knot invariant, providing an estimation for the slice genus of the knot and a new proof of Milnor's conjecture. This conjecture was previously accessible only via gauge theory: instanton Donaldson invariants originally, then Seiberg-Witten theory, and finally the Ozsvath-Szabo Heegaard Floer Homology. The aim of the project is to extend the Khovanov construction to 3-manifolds and to compare the result with the Heegaard Floer Homology of Ozsvath and Szabo. |
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| Publications / Publikationen | Beliakova, Anna; Wehrli, Stephan: Categorification of the colored Jones polynomial and Rasmussen invariant of links, Canad. J. Math. 60 (2008), no. 6, 1240--1266Wehrli, Stephan M.: A spanning tree model for Khovanov homology, J. Knot Theory Ramifications 17 (2008), no. 12, 1561-1574Wehrli, Stephan M.: Khovanov Homology and Conway Mutation, arXiv:math.GT/0301312Beliakova, Anna: A simplification of combinatorial link Floer Homology, J. Knot Theory Ramifications, (2010) v.3 Obervolfach Proceedings, 1--20Beliakova, Anna; Wagner, Emmanuel: On Link Homology Theories from Extended Cobordisms, arXiv:0910.5050Droz, Jean-Marie: Effective computation of knot Floer homology, arXiv:0803.2379Weitere Informationen |
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| Project leadership and contacts / Projektleitung und Kontakte |
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| Funding source(s) / Unterstützt durch |
SNF (Personen- und Projektförderung), SNF (Programm NFS/NCCR) |
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| In collaboration with / In Zusammenarbeit mit |
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| Duration of Project / Projektdauer | Apr 2004 to Sep 2013 |