## 2005.34: Homotopy Decompositions and K-theory of Bott Towers

2005.34:
Yusuf Civan and Nigel Ray
(2004)
*Homotopy Decompositions and K-theory of Bott Towers.*
K-theory, 34 (1).
pp. 1-33.
ISSN 0920-3036

Full text available as:

PDF - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader 316 Kb |

DOI: 10.1007/s10977-005-1551-x

## Abstract

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 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 analysis of the Adams Spectral Sequence. By way of application we consider the enumeration of stably complex structures on M^k, obtaining estimates for 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.

Item Type: | Article |
---|---|

Uncontrolled Keywords: | Bott towers, K-Theory, stably complex structures, Thom complexes, toric manifolds |

Subjects: | MSC 2000 > 55 Algebraic topology MSC 2000 > 57 Manifolds and cell complexes |

MIMS number: | 2005.34 |

Deposited By: | Nigel Ray |

Deposited On: | 09 December 2005 |

Download Statistics: last 4 weeks

Repository Staff Only: edit this item