Timeline for Topological connected eccentrics, not homeomorphic to commutative Lie groups
Current License: CC BY-SA 4.0
3 events
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| May 20, 2020 at 11:51 | comment | added | YCor | PS in this paper (M. Choban, L. Chiriac, Selected problems and results of topological algebra, Romai J., v.9, no.1(2013), 1–25, ), it is stated that among spheres, only those of dimension $0,1,3,7$ admit a topological quasigroup structure (that is, a topological E-structure). | |
| May 20, 2020 at 7:13 | comment | added | YCor | In general a on a (compact) closed topological manifold $X$ an E-structure is the same as a continuous map $i:X\to\mathrm{Homeo}(X)$ such that for any distinct $x,y\in X$, $i(x)^{-1}i(y)$ has no fixed point. Just the property of admitting uncountably many self-homeomorphism pairwise with no common fixed point is restrictive: among spheres it selects odd-dimensional ones. Among surfaces it only selects the 2-torus and the Klein bottle. So far I'm unable to figure out whether the Klein bottle or the 5-sphere admit such structures, anyway. | |
| May 20, 2020 at 6:37 | history | answered | YCor | CC BY-SA 4.0 |