Torus Manifolds in Equivariant Complex Bordism

2014/09/09 by Darby, Alastair
#57R85 #Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.1409.2720

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.

Related

• Equivariant Bordism of 2-Torus Manifolds and Unitary Toric Manifolds
• Geometric versus homotopy theoretic equivariant bordism
• Bordism and resolution of singularities
• Tangential Structures on Toric Manifolds, and Connected Sums of Polytopes
• Computations of Complex Equivariant Bordism Rings