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arXiv · 1409.2720

Torus Manifolds in Equivariant Complex Bordism

Alastair Darby
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Abstract

We restrict geometric tangential equivariant complex $T^n$-bordism to torus manifolds and provide a complete combinatorial description of the appropriate non-commutative ring. We discover, using equivariant $K$-theory characteristic numbers, that the information encoded in the oriented torus graph associated to a stably complex torus manifold completely describes its equivariant bordism class. We also consider the role of omnioriented quasitoric manifolds in this description.

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Alastair Darby. 2014-09-09. Torus Manifolds in Equivariant Complex Bordism. https://arxiv.org/abs/1409.2720

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