Doman Takata

activity

20152026

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math.KT2026

Geometric $K$ -homology and operator $K$ -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…

math.KT2022

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…

math.KT2020

Topological Aspects of the Equivariant Index Theory of Infinite-Dimensional LT-Manifolds

Doman Takata

Let $T$ be the circle group and let $L T$ be its loop group. We formulate and investigate several topological aspects of the $L T$ -equivariant index theory for proper $L T$ -spaces, wh…

math.KT2017

LT-equivariant Index from the Viewpoint of KK-theory

Doman Takata

Let $T$ be a circle group, and $L T$ be its loop group. We hope to establish an index theory for infinite-dimensional manifolds which $L T$ acts on, including Hamiltonian $L T$ -spaces…

math.KT2015

Naturality of FHT isomorphism

Doman Takata

Freed, Hopkins and Teleman constructed an isomorphism between twisted equivariant K-theory of compact Lie group $G$ and the "Verlinde ring" of the loop group of $G$ . We call this i…

Geometric K-homology and operator K-theory for Hilbert manifolds

Seiberg-Witten theory on finite covering spaces of spin 4-manifolds

Topological Aspects of the Equivariant Index Theory of Infinite-Dimensional LT-Manifolds

LT-equivariant Index from the Viewpoint of KK-theory

Naturality of FHT isomorphism

Geometric $K$ -homology and operator $K$ -theory for Hilbert manifolds