The KO-theory of toric manifolds

Citation
A. Bahri et M. Bendersky, The KO-theory of toric manifolds, T AM MATH S, 352(3), 2000, pp. 1191-1202
Citations number
9
Categorie Soggetti
Mathematics
Journal title
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
ISSN journal
00029947 → ACNP
Volume
352
Issue
3
Year of publication
2000
Pages
1191 - 1202
Database
ISI
SICI code
0002-9947(200003)352:3<1191:TKOTM>2.0.ZU;2-D
Abstract
Toric manifolds, a topological generalization of smooth projective toric va rieties, are determined by an n-dimensional simple convex polytope and a fu nction from the set of codimension-one faces into the primitive vectors of an integer lattice. Their cohomology was determined by Davis and Januszkiew icz in 1991 and corresponds with the theorem of Danilov-Jurkiewicz in the t oric variety case. Recently it has been shown by Buchstaber and Ray that th ey 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.