Homotopy decompositions and K-theory of bott towers

Civan Y. , Ray N.

K-THEORY, vol.34, no.1, pp.1-33, 2005 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 34 Issue: 1
  • Publication Date: 2005
  • Doi Number: 10.1007/s10977-005-1551-x
  • Title of Journal : K-THEORY
  • Page Numbers: pp.1-33


We describe Bott towers as sequences of toric manifolds M-k, and identify the omniorientations which correspond to their original construction as complex 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 K O-theory for several families of examples, and compute the effects of the realication homomorphism; these calculations breathe geometric life into Bahri and Bendersky's analysis of the Adams Spectral Sequence [ Bahri, A. and Bendersky, M.: The KO-theory of toric manifolds. Trans. Am. Math. Soc. 352 ( 2000), 1191 - 1202.] By way of application we consider the enumeration of stably complex structures on Mk, obtaining estimates for those which arise from omniorientations and those which are almost complex. We conclude with observations on the r (o) over cap le of Bott towers in complex cobordism theory.