2010 Fiscal Year Final Research Report
Extensions of topological quantum field theories by means of categorification of geometric quantization
Project/Area Number |
21840034
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Research Category |
Grant-in-Aid for Research Activity Start-up
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Allocation Type | Single-year Grants |
Research Field |
Geometry
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Research Institution | Kyoto University |
Principal Investigator |
GOMI Kiyonori Kyoto University, 大学院・理学研究科, 准教授 (00543109)
|
Project Period (FY) |
2009 – 2010
|
Keywords | 位相的量子場の理論 / 幾何的量子化 / Chern-Simons理論 / gerbe / twisted K-theory / differential K-theory |
Research Abstract |
(i) Developing my results so far, I got a finite-dimensional realization of equivariant twisted K-cohomology theory. In particular, this realization allows that by using actions of Clifford algebras. (ii) I constructed a basis of the ring of universal characteristic classes for twisted K-theory of certain type. By means of this basis, I gave a new lift to twisted de Rham cohomology. (iii) I proved that an operation defined by the product in differential K-theory factors through a single delooping of an Adams operation.
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