Timeline for Can both G and BG be finite CW complexes?
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| Oct 9, 2013 at 18:59 | comment | added | Jesper Grodal | The limitation of this answer (contrary to Tom's) is that it takes a strict definition of "is" in "is a finite CW complex". Namely you take it to mean "homeomorphic to" rather than "homotopy equivalent to". A finite loop space is a space homotopy equivalent to both a topological group and a finite CW complex. These need not in general be homotopy equivalent to compact Lie groups -- see e.g., section 3 of my survey paper math.ku.dk/~jg/papers/icm.pdf for a summary. | |
| Oct 2, 2013 at 23:05 | comment | added | David E Speyer | @MarianoSuárez-Alvarez Thanks, that's what I meant to write. | |
| Oct 2, 2013 at 23:05 | history | edited | David E Speyer | CC BY-SA 3.0 |
added 16 characters in body
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| Oct 2, 2013 at 23:03 | comment | added | Mariano Suárez-Álvarez | WHat is useful is that the interior of every top dimensional cell is a topological manifold, no? To conclude that $%\chi(G)=0$ it is simplest to use the fact that $G$ is paralellizable, maybe. | |
| Oct 2, 2013 at 22:54 | history | answered | David E Speyer | CC BY-SA 3.0 |