Torus manifolds in equivariant complex bordism

Alastair Darby

doi:10.1016/j.topol.2015.03.014

Torus manifolds in equivariant complex bordism

Alastair Darby^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

We restrict geometric tangential equivariant complex Tⁿ-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.

Original language	English
Pages (from-to)	31-64
Number of pages	34
Journal	Topology and its Applications
Volume	189
DOIs	https://doi.org/10.1016/j.topol.2015.03.014
Publication status	Published - 1 Jul 2015
Externally published	Yes

Keywords

Equivariant cobordism
Toric topology

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10.1016/j.topol.2015.03.014

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title = "Torus manifolds in equivariant complex bordism",

abstract = "We restrict geometric tangential equivariant complex Tn-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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AB - We restrict geometric tangential equivariant complex Tn-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.

KW - Equivariant cobordism

KW - Toric topology

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DO - 10.1016/j.topol.2015.03.014

M3 - Article

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VL - 189

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JO - Topology and its Applications

JF - Topology and its Applications

ER -

Torus manifolds in equivariant complex bordism

Abstract

Keywords

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