Timeline for Infinite dimensional homology theory for submanifolds of Hilbert and Banach spaces
Current License: CC BY-SA 4.0
3 events
| when toggle format | what | by | license | comment | |
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| Aug 29, 2023 at 20:27 | comment | added | Denis T | One direction to go would be only allowing smooth (...and here you need to choose among several notions of smoothness in Frechet, and even Banach case) homotopies and tryin to do axiomatic Steenrod homology; but then representability of this thing by some functorial complex of TVS would be a miracle. | |
| Aug 29, 2023 at 20:22 | comment | added | Denis T | Well, there's a theorem by Palais that says that every Hilbert (or, equivalently, Frechet) manifold - a space locally homeomorphic to an open subset of a separable Hilbert space - is an ANR homotopy equivalent to a locally finite countable CW complex. So unless you go into something like differential (co)homology setting and let go of usual homotopy invariance, you get nothing new. | |
| Aug 29, 2023 at 19:05 | history | asked | 0x11111 | CC BY-SA 4.0 |