The $KO$-theory of toric manifolds
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- by Anthony Bahri and Martin Bendersky PDF
- Trans. Amer. Math. Soc. 352 (2000), 1191-1202 Request permission
Abstract:
Toric manifolds, a topological generalization of smooth projective toric varieties, are determined by an $n$-dimensional simple convex polytope and a function from the set of codimension-one faces into the primitive vectors of an integer lattice. Their cohomology was determined by Davis and Januszkiewicz in 1991 and corresponds with the theorem of Danilov-Jurkiewicz in the toric variety case. Recently it has been shown by Buchstaber and Ray that they generate the complex cobordism ring. We use the Adams spectral sequence to compute the $KO$-theory of all toric manifolds and certain singular toric varieties.References
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Additional Information
- Anthony Bahri
- Affiliation: Department of Mathematics, Rider University, Lawrenceville, New Jersey 08648
- Email: bahri@rider.edu
- Martin Bendersky
- Affiliation: Department of Mathematics, Hunter College, New York, New York 10021
- Email: mbenders@shiva.hunter.cuny.edu
- Received by editor(s): September 17, 1997
- Published electronically: July 26, 1999
- © Copyright 1999 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 352 (2000), 1191-1202
- MSC (1991): Primary 55N15, 55T15, 14M25, 19L41; Secondary 57N65
- DOI: https://doi.org/10.1090/S0002-9947-99-02314-4
- MathSciNet review: 1608269