Timeline for Bijection homotopy class of maps and homomorphisms of fundamental group
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 28, 2017 at 15:56 | comment | added | Max Power | I am mainly using Husemoller's book, where he introduces the Milnor Construction as universal bundle in chapter 4. In Excercise 13 he asserts that the total space of a universal bundle is contractible, which implies that the basis space is Eilenberg-MacLane for discrete groups. As suggested, I would like to use e.g. Proposition 1B.9 in Hatchers book, which gives the demanded bijection only for CW complexes. But what is the cell structure of the Milnor Construction? Milnor's total space looks similar to the construction in Hatcher's book, but I don't see why the topology is the same. | |
| Aug 28, 2017 at 13:03 | answer | added | Nick L | timeline score: 2 | |
| Aug 28, 2017 at 9:36 | comment | added | Max Power | @MichaelAlbanese I'm interested in the discrete case first, though I would like to hear why it fails for the general case. | |
| Aug 27, 2017 at 18:44 | comment | added | Michael Albanese | @MaxMustermann: Given your general question, you seem to be under the impression that $\pi_1(BG) \cong G$. This is only true if $G$ is discrete. Are you asking only about the discrete case, or in general? | |
| Aug 27, 2017 at 18:18 | comment | added | Gregory Arone | For the first question see Hatcher, Proposition 1B.9 on page 90 (it is pointed homotopy classes of maps). | |
| Aug 27, 2017 at 17:57 | history | asked | Max Power | CC BY-SA 3.0 |