Timeline for Was homology influenced by Euler's polyhedron formula?
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Aug 5 at 9:07 | comment | added | ThiKu | I think so, yes. | |
| Aug 5 at 6:13 | comment | added | user1274233 | Hello, thank you very much for your answer. Then, can I think of the significance of Poincaré's proof as follows in this file? Poincaré (1854-1912) gave a definition of the Euler- Poincaré characteristic for arbitrary polyhedra, and one proves now, by invoking the topological invariance of the homology groups that the Euler-Poincare characteristic is a topological invariant. | |
| Aug 4 at 10:19 | vote | accept | user1274233 | ||
| Aug 4 at 9:40 | comment | added | ThiKu | Hilton and Pedersen in numdam.org/article/SPHM_1982___8_A1_0.pdf attribute to Poincaré the definition of the Euler characteristics for simplicial complexes, but say that the proof of the Euler formula in this setting follows from topological invariance of homology. (Which of course was not known at Poincaré’s time.) | |
| Aug 4 at 9:33 | comment | added | ThiKu | Hopf’s original proof seems to be the one in zbmath.org/55.0970.02 | |
| Aug 4 at 9:32 | comment | added | ThiKu | Thank you, I have edited my answer accordingly. | |
| Aug 4 at 9:31 | history | edited | ThiKu | CC BY-SA 4.0 |
added 630 characters in body
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| Aug 4 at 8:28 | comment | added | Sam Nead | +1 for this answer. It got me to do some searching and I found Hirzebruch's very nice article Emmy Noether and topology. He refers to Hopf's article Eine Verallgemeinerung der Euler-Poincaréschen Formel. However, Hopf's comments are not transparent to me - perhaps he had a version of Euler's formula before Noether, but he only had a nice proof only after Noether?? | |
| Aug 4 at 7:54 | history | answered | ThiKu | CC BY-SA 4.0 |