Homotopy decompositions and K-theory of Bott towers

2004/08/19 by Yusuf Civan, Civan, Yusuf, Nigel Ray +1
Mathematics · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #math.AT #msc:55N15 #msc:57N65

paper · pdf · doi:10.48550/arxiv.math/0408261

26 pages

arxiv created 2004/08/19 · arxiv updated 2009/12/01

Abstract

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.

Citations

• Bott towers, complete integrability, and the extended character of representations

Related

• Bott towers, crosspolytopes and torus actions
• Topological classification of generalized Bott towers
• Some results on the topology of real Bott towers
• Tangential Structures on Toric Manifolds, and Connected Sums of Polytopes
• The KO-theory of Toric Manifolds