2 citations · 2 across the 6 of their papers we have counts for
8 papers
Geometric -homology and operator -theory for Hilbert manifolds
Doman Takata
Poincaré duality is a classical theorem relating the homology and cohomology of closed oriented manifolds. This theorem has been extended to more general settings and to generalize…
An Index Theorem for Loop Spaces
Doman Takata
We formulate and prove an index theorem for loop spaces of compact manifolds in the framework of -theory. It is a strong candidate for the noncommutative geometrical definition…
Seiberg-Witten theory on finite covering spaces of spin 4-manifolds
Tsuyoshi Kato, Doman Takata
We compute the equivariant Bauer-Furuta degree, when a finite group acts freely on a spin 4-manifold. In the case when the group is cyclic of order power of two, Bryan gave a formu…
Topological Aspects of the Equivariant Index Theory of Infinite-Dimensional LT-Manifolds
Doman Takata
Let be the circle group and let be its loop group. We formulate and investigate several topological aspects of the -equivariant index theory for proper -spaces, wh…
An infinite-dimensional index theorem and the Higson-Kasparov-Trout algebra
Doman Takata
We have been studying the index theory for some special infinite-dimensional manifolds with a "proper cocompact" actions of the loop group LT of the circle T, from the viewpoint of…
LT-equivariant Index from the Viewpoint of KK-theory
Doman Takata
Let be a circle group, and be its loop group. We hope to establish an index theory for infinite-dimensional manifolds which acts on, including Hamiltonian -spaces…
An Analytic LT-equivariant Index and Noncommutative Geometry
Doman Takata
Let be a circle and be its loop group. Let be an infinite dimensional manifold equipped with a nice -action. We construct an analytic -equivariant in…
Naturality of FHT isomorphism
Doman Takata
Freed, Hopkins and Teleman constructed an isomorphism between twisted equivariant K-theory of compact Lie group and the "Verlinde ring" of the loop group of . We call this i…