Minimal homeomorphisms and topological K-theory

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F23%3A00573356" target="_blank" >RIV/67985840:_____/23:00573356 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.4171/ggd/707" target="_blank" >https://doi.org/10.4171/ggd/707</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4171/GGD/707" target="_blank" >10.4171/GGD/707</a>

Result language
angličtina
Original language name
Minimal homeomorphisms and topological K-theory
Original language description
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. Minimal homeomorphisms are constructed on compact connected metric spaces with any prescribed finitely generated K-theory or cohomol-ogy. In particular, although a non-zero Euler characteristic obstructs the existence of a minimal homeomorphism on a finite CW-complex, this is not the case on a compact metric space. 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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GJ20-17488Y" target="_blank" >GJ20-17488Y: Applications of C*-algebra classification: dynamics, geometry, and their quantum analogues</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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