K-theory of torus manifolds

Details K-theory of torus manifolds K-theory of torus manifolds

2006-07-31

arxiv.org/abs/math/0607804v1

Mathematics

Algebraic Topology

5 pages

Scientific paper

The {\it torus manifolds} have been defined and studied by M. Masuda and T. Panov (arXiv:math.AT/0306100) who in particular describe its cohomology ring structure. In this note we shall describe the topological $K$-ring of a class of torus manifolds (those for which the orbit space under the action of the compact torus is a {\it homology polytope} whose {\it nerve} is a {shellable} simplicial complex) in terms of generators and relations. Since these torus manifolds include the class of quasi-toric manifolds this is a generalisation of earlier results due to the author and P. Sankaran (arXiv: math.AG/0504107).

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