$AF$-algebras and topology of mapping tori

Czechoslovak Mathematical Journal

Igor Nikolaev¹ 

[1] The Fields Institute for Research in Mathematical Sciences, University of Toronto, College Street 222, Toronto, Ontario, M5T 3J1, Canada

关键词: Anosov diffeomorphism;    $AF$-algebra;   

DOI  :  

学科分类：数学（综合）

来源: Akademie Ved Ceske Republiky

【 摘 要 】

The paper studies applications of $C^*$-algebras in geometric topology. Namely, a covariant functor from the category of mapping tori to a category of $AF$-algebras is constructed; the functor takes continuous maps between such manifolds to stable homomorphisms between the corresponding $AF$-algebras. We use this functor to develop an obstruction theory for the torus bundles of dimension $2$, $3$ and $4$. In conclusion, we consider two numerical examples illustrating our main results.

【 授权许可】

Unknown