Timeline for Homotopy Equivalences and Induced Correspondences between Fibre Bundles
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 19, 2013 at 16:34 | comment | added | Ronnie Brown | @Ricardo: Thanks for your interest. I'll also mention that the proof of the gluing theorem in all editions of my book was found by generalising the proof that a homotopy equivalence (not necessarily based) of spaces induces an isomorphism of homotopy groups. It is this that leads to the control of the homotopies. | |
| Mar 1, 2013 at 22:45 | comment | added | Ricardo Andrade | @PDC: It was my pleasure. | |
| Mar 1, 2013 at 22:26 | comment | added | Ricardo Andrade | @Ronnie: Thank you very much for your comment. I had actually heard that before about the Hurewicz theorem in Spanier's book, but had forgotten about it. I must admit I have never checked that section of Spanier's book --- along with many other sections :). Also, I was not aware of the original references for the right properness of the Strom model structure. Thanks! | |
| Mar 1, 2013 at 16:18 | comment | added | Peter Crooks | This is fantastic advice! I really appreciate the input from each of you! | |
| Mar 1, 2013 at 14:40 | comment | added | Ronnie Brown | (ran out of space, so continue) ``Coglueing homotopy equivalences'', Math. Z. 113 (1970) 313-362. This was taken as the dual of the "glueing theorem" in the 1968 edition of my book now available as "Topology and Groupoids". These proofs have the advantage of giving control over the homotopies involved. | |
| Mar 1, 2013 at 14:35 | comment | added | Ronnie Brown | With regard to Spanier's book p. 95 (first edition) he defines a few lines above 12 Theorem an "extended lifting function" $\Lambda". I suggested a to him another formula to make sure the functionwas well defined, and this appeared in the second edition. But I confess I gave up trying to prove this modified function was continuous. Has anyone written out a proof? I also refer people to the paper by Dyer and Eilenberg, Globalizing fibrations by schedules. Fund. Math. 130 (1988), 125--136. The right pro-perness for Hurewicz fibrations was first observed, I think, in R. Brown and P.R. | |
| Mar 1, 2013 at 9:24 | history | edited | Ricardo Andrade | CC BY-SA 3.0 |
edited body
|
| Mar 1, 2013 at 5:02 | history | edited | Ricardo Andrade | CC BY-SA 3.0 |
improved formatting
|
| Mar 1, 2013 at 4:05 | history | edited | Ricardo Andrade | CC BY-SA 3.0 |
deleted 622 characters in body
|
| Mar 1, 2013 at 3:49 | history | edited | Ricardo Andrade | CC BY-SA 3.0 |
added 6 characters in body
|
| Mar 1, 2013 at 3:41 | history | answered | Ricardo Andrade | CC BY-SA 3.0 |