Minimal homeomorphisms and topological $K$-theory
Dynamical Systems
2022-02-02 v2 Operator Algebras
Abstract
The Lefschetz fixed point theorem provides a powerful obstruction to the existence of minimal homeomorphisms on well-behaved spaces such as finite CW-complexes. We show that these obstructions do not hold for more general spaces. More precisely, minimal homeomorphisms are constructed on space with prescribed -theory or cohomology. We also allow for some control of the map on -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 -algebras will be discussed in another paper.
Cite
@article{arxiv.2012.10950,
title = {Minimal homeomorphisms and topological $K$-theory},
author = {Robin J. Deeley and Ian F. Putnam and Karen R. Strung},
journal= {arXiv preprint arXiv:2012.10950},
year = {2022}
}
Comments
27 pages. To appear in Groups, Geom. Dyn. This supersedes arXiv:1907.03851, which will not be submitted for publication