Minimal homeomorphisms and topological K K K -theory

[摘要] The Lefschetz fixed point theorem provides a powerful obstruction to the existence of minimal homeomorphisms on well-behaved spaces such as finite CWCWCW-complexes. We show that these obstructions do not hold for more general spaces. Minimal homeomorphisms are constructed on compact connected metric spaces with any prescribed finitely generated KKK-theory or cohomology. In particular, although a non-zero Euler characteristic obstructs the existence of a minimal homeomorphism on a finite CWCWCW-complex, this is not the case on a compact metric space. We also allow for some control of the map on KKK-theory and cohomology induced from these minimal homeomorphisms. This allows for the construction of many minimal homeomorphisms that are not homotopic to the identity. Applications to C∗C^*C∗-algebras will be discussed in another paper.

[学科分类] 神经科学

[关键词] Minimal homeomorphisms;K-theory;classification of nuclear C -algebras