Homotopy decompositions and K-theory of Bott towers

Details Homotopy decompositions and K-theory of Bott towers Homotopy decompositions and K-theory of Bott towers

2004-08-19

arxiv.org/abs/math/0408261v1

Mathematics

Algebraic Topology

26 pages

Scientific paper

We describe Bott towers as sequences of toric manifolds M^k, and identify the omniorientations which correspond to their original construction as toric varieties. We show that the suspension of M^k is homotopy equivalent to a wedge of Thom complexes, and display its complex K-theory as an algebra over the coefficient ring. We extend the results to KO-theory for several families of examples, and compute the effects of the realification homomorphism; these calculations breathe geometric life into Bahri and Bendersky's recent analysis of the Adams Spectral Sequence. By way of application we investigate stably complex structures on M^k, identifying those which arise from omniorientations and those which are almost complex. We conclude with observations on the role of Bott towers in complex cobordism theory.

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