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- W2084179520 abstract "We study low-dimensional problems in topology and geometry via a study of contact and Cauchy-Riemann ($CR$) structures. A contact structure is called spherical if it admits a compatible spherical $CR$ structure. We will talk about spherical contact structures and our analytic tool, an evolution equation of $CR$ structures. We argue that solving such an equation for the standard contact 3-sphere is related to the Smale conjecture in 3-topology. Furthermore, we propose a contact analogue of Ray-Singer's analytic torsion. This ''contact torsion'' is expected to be able to distinguish among ''spherical space forms'' ${Gammabackslash S^{3}}$ as contact manifolds. We also propose the study of a certain kind of monopole equation associated with a contact structure. In view of the recently developed theory of contact homology algebras, we will discuss its overall impact on our study." @default.
- W2084179520 created "2016-06-24" @default.
- W2084179520 creator A5042146046 @default.
- W2084179520 date "2001-06-11" @default.
- W2084179520 modified "2023-09-27" @default.
- W2084179520 title "Contact topology and CR geometry in three dimensions" @default.
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