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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The $KO$-theory of toric manifolds


Authors: Anthony Bahri and Martin Bendersky
Journal: Trans. Amer. Math. Soc. 352 (2000), 1191-1202
MSC (1991): Primary 55N15, 55T15, 14M25, 19L41; Secondary 57N65
Published electronically: July 26, 1999
MathSciNet review: 1608269
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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.


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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

DOI: http://dx.doi.org/10.1090/S0002-9947-99-02314-4
PII: S 0002-9947(99)02314-4
Keywords: Toric manifolds, toric varieties, $KO$-theory, Adams spectral sequence.
Received by editor(s): September 17, 1997
Published electronically: July 26, 1999
Article copyright: © Copyright 1999 American Mathematical Society