Timeline for Coarse index of Dirac operator on $\mathbb{R}$
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
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| Jun 17, 2019 at 9:24 | vote | accept | geometricK | ||
| Jun 15, 2019 at 17:29 | comment | added | Paul Siegel | The assertion that the ordinary K-homology boundary map sends the Dirac class to $1$ is basically proposition 9.6.6 in Higson and Roe's Analytic K-homology, though the proof with all details uses most of the machinery built in chapters 8 and 9. Passing from this to a calculation with Mayer-Vietoris boundary maps is sort of folk wisdom in operator K-theory; I honestly don't know a place where it's all written out other than my PhD thesis, available here: pwsiegel.github.io/resources/paul-siegel-phd-thesis.pdf. This is not a claim of priority; someone else might know another reference. | |
| Jun 15, 2019 at 15:31 | comment | added | geometricK | Thanks - do you have a reference for the difficult but standard calculation that you refer to, showing that the $K$-homology class of the Dirac operator on $\mathbb{R}$ maps to an operator of index $1$ under $MV$? | |
| Jun 11, 2019 at 7:30 | history | answered | Paul Siegel | CC BY-SA 4.0 |