Minimal homeomorphisms and topological $K$-theory

Autor:	Deeley, Robin J., Putnam, Ian F., Strung, Karen R.
Rok vydání:	2020
Předmět:	Mathematics - Dynamical Systems Mathematics - Operator Algebras 37B05 19L99
Druh dokumentu:	Working Paper
Popis:	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 $K$-theory or cohomology. We also allow for some control of the map on $K$-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 $C^*$-algebras will be discussed in another paper. Comment: 27 pages. To appear in Groups, Geom. Dyn. This supersedes arXiv:1907.03851, which will not be submitted for publication
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2012.10950 Zobrazit plný text záznamu View this record from Arxiv