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This article is cited in 43 scientific papers (total in 44 papers)
Spaces of polytopes and cobordism of quasitoric manifolds
V. M. Buchstabera, T. E. Panovb, N. Rayc a Steklov Mathematical Institute, Russian Academy of Sciences
b M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
c University of Manchester, Department of Mathematics
Abstract:
Our aim is to bring the theory of analogous polytopes to bear on the study of quasitoric manifolds, in the context of stably complex manifolds with compatible torus action. By way of application, we give an explicit construction of a quasitoric representative for every complex cobordism class as the quotient of a free torus action on a real quadratic complete intersection. We suggest a systematic description for omnioriented quasitoric manifolds in terms of combinatorial data, and explain the relationship with non-singular projective toric varieties (otherwise known as toric manifolds). By expressing the first and third authors' approach to the representability of cobordism classes in these terms, we simplify and correct two of their original proofs concerning quotient polytopes; the first relates to framed embeddings in the positive cone, and the second involves modifying the operation of connected sum to take account of orientations. Analogous polytopes provide an informative setting for several of the details.
Key words and phrases:
Analogous polytopes, complex cobordism, connected sum, framing, omniorientation, quasitoric manifold, stable tangent bundle.
Received: September 15, 2006
Citation:
V. M. Buchstaber, T. E. Panov, N. Ray, “Spaces of polytopes and cobordism of quasitoric manifolds”, Mosc. Math. J., 7:2 (2007), 219–242
Linking options:
https://www.mathnet.ru/eng/mmj280 https://www.mathnet.ru/eng/mmj/v7/i2/p219
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