t-cat
The t-cat of a topological space^{} $X$ is the minimal number of open sets that cover $X$ such that each open set in the cover has the homotopy type^{} of the unit circle ${S}^{1}$. This means that for each open set $U$, the inclusion $U\stackrel{i}{\hookrightarrow}X$ is homotopic^{} to some factorization $U\stackrel{a}{\to}{S}^{1}\stackrel{b}{\to}X$, i.e.
$$i\simeq b\circ a.$$ |
When $X$ is manifold^{}, this is related to the round complexity of $X$.
References
- 1 D. Siersma, G. Khimshiasvili, On minimal^{} round functions, Preprint 1118, Department of Mathematics, Utrecht University, 1999, pp. 18.
Title | t-cat |
---|---|
Canonical name | Tcat |
Date of creation | 2013-03-22 15:54:54 |
Last modified on | 2013-03-22 15:54:54 |
Owner | juanman (12619) |
Last modified by | juanman (12619) |
Numerical id | 7 |
Author | juanman (12619) |
Entry type | Definition |
Classification | msc 55M30 |
Related topic | RoundComplexity |