2012 Fiscal Year Final Research Report
Research on knot theory using contact structures and holomorphic curves
| Project/Area Number |
21740041
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Geometry
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| Research Institution | Tokyo Institute of Technology (2010-2012)
The University of Tokyo (2009) |
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Principal Investigator |
KALMAN Tamas 東京工業大学, グローバルエッジ研究院, テニュア・トラック助教 (00534041)
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| Project Period (FY) |
2009 – 2012
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| Keywords | 微分トポロジー |
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| Research Abstract |
In this research, I developed a theory that describes a surprising new relation between Heegaard Floer homology and the Homfly polynomial. The connection is well understood in the case of special alternating links, with partial results toward a generalization to all oriented links. It uses a theory in algebraic combinatorics (on hypertrees, polymatroids, and their interior polynomials) that I developed and which is very interesting in its own right. In joint work with Juhasz and Rasmussen, we related these notions to Heegaard Floer homology, and in joint work with Murakami, we described their connection to quantum invariants. All these works were presented at conferences both inside and outside of Japan, and with the exception of the joint work with Murakami, they were published in refereed journals.
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