Timeline for Computing homotopies
Current License: CC BY-SA 2.5
19 events
| when toggle format | what | by | license | comment | |
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| Jun 1, 2013 at 20:45 | comment | added | Ronnie Brown | @Fernando: The proof in my book "Topology and Groupoids" (first edition 1968) of "cofiber homotopy equivalence" is derived from the classic proof that a homotopy equivalence of spaces induces an isomorphism of homotopy groups. What I did is generalise from the case $(S^n,1)$ to the case of $(Z,A)$ having the HEP. To carry this out one generalises operation of the fundamental groupoid to operations of a track groupoid. The "segment formulae" come in giving examples of the HEP. As Peter wrote in "Concise...", my book is "idiosyncratic", perhaps in its generality! | |
| May 31, 2013 at 10:08 | comment | added | Fernando Muro | @Benjamin, I completely agree with you. I got my math degree at a place with much emphasis in analysis, so when I started learning algebraic topology I felt very uneasy about descriptions of homotopies without analytic formulas, but it's the most reasonable way of doing things and should be promoted. | |
| May 30, 2013 at 17:23 | comment | added | Benjamin Steinberg | Homotopies are a bit like Turing Machines: one should always give a high-level description because it is almost impossible to figure out what it is doing when written formally. | |
| May 30, 2013 at 10:26 | comment | added | Fernando Muro | In my experience, all homotopies are variations of the segment $H(t)=tP+(1-t)Q$. | |
| May 30, 2013 at 10:06 | answer | added | Ronnie Brown | timeline score: 6 | |
| Feb 5, 2011 at 0:05 | vote | accept | Harry Gindi | ||
| Feb 4, 2011 at 2:47 | answer | added | Peter May | timeline score: 19 | |
| Jan 6, 2011 at 11:18 | vote | accept | Harry Gindi | ||
| Feb 5, 2011 at 0:05 | |||||
| Jan 4, 2011 at 17:07 | answer | added | Jeff Strom | timeline score: 8 | |
| Jan 4, 2011 at 16:15 | answer | added | Bill Thurston | timeline score: 58 | |
| Jan 4, 2011 at 16:14 | comment | added | Kevin Walker | Harry, for what it's worth I agree that these explicit homotopies are slightly annoying. | |
| Jan 4, 2011 at 14:15 | history | edited | Harry Gindi | CC BY-SA 2.5 |
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| Jan 4, 2011 at 13:54 | answer | added | Tom Goodwillie | timeline score: 16 | |
| Jan 4, 2011 at 10:16 | history | edited | Harry Gindi | CC BY-SA 2.5 |
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| Jan 4, 2011 at 9:30 | comment | added | Harry Gindi | Dear Patrick, look at May's proof of cofiber homotopy equivalence, for instance. | |
| Jan 4, 2011 at 9:26 | comment | added | Patrick I-Z | Hi Harry, I meant an example of "little formulas pulled out" ? | |
| Jan 4, 2011 at 9:11 | comment | added | Harry Gindi | Dear Patrick, I think I gave an example. Could you clarify what more you would like to hear? | |
| Jan 4, 2011 at 9:06 | comment | added | Patrick I-Z | Can you give an example ? | |
| Jan 4, 2011 at 8:37 | history | asked | Harry Gindi | CC BY-SA 2.5 |