Minimal homeomorphisms and topological K-theory

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Minimal homeomorphisms and topological K-theory

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Minimal homeomorphisms and topological K-theory

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GJ20-17488Y" target="_blank" >GJ20-17488Y: Aplikace klasifikace C*-algeber: dynamika, geometrie a jejich kvantové analogie</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2023

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Groups Geometry and Dynamics

ISSN

1661-7207

e-ISSN

1661-7215

Svazek periodika

17

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

32

Strana od-do

501-532

Kód UT WoS článku

000989157100006

EID výsledku v databázi Scopus

2-s2.0-85163772355