Timeline for Reference: Betti Numbers of the free loop space are finite
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Feb 28, 2022 at 7:47 | comment | added | Mark Grant | In the non-simply connected case you can easily have infinite $0$-th and $1$-st Betti numbers, e.g. if $\pi_1(M)=\mathbb{Z}$ then $\Lambda M$ has infinitely many path components. Not sure about the higher Betti numbers. | |
| Feb 27, 2022 at 23:15 | comment | added | user188722 | Hi Mark, can I ask a question - does this finiteness of Betti number hold only for simply connected manifolds? How about non-simply connected ones? | |
| Sep 16, 2015 at 12:53 | comment | added | Sinan Yalin | Concerning the growth of Betti numbers of free loop spaces, it is worth mentionning also the papers of Pascal Lambrechts On the Betti numbers of the free loop space of a coformal space (JPAA 2001) and The Betti numbers of the free loop space of a connected sum ( J. London Math. Soc. 2001). | |
| Sep 16, 2015 at 12:42 | history | answered | Mark Grant | CC BY-SA 3.0 |