Timeline for Is there a derived geometric interpretation of morse functions?
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| when toggle format | what | by | license | comment | |
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| Jul 22, 2017 at 12:12 | comment | added | Saal Hardali | The hessian can be defined in a completely algebraic manner at a singular point ($df=0$). Without loss of generality assume $f=0$ at the critical point. Consider the 2nd order jet sequence $0 \to Sym^2 \mathcal{T}^*_X \to \mathcal{J}^2 \to \mathcal{J}^1 \to 0$. Since the 1-st order jet vanishes at the critical point $f$ defines a unique symmteric bilinear form on the tangent space. Regarding the second part it depends what you mean by "poincare polynomial. There are many cohomology theories for smooth affine schemes. | |
| Sep 6, 2016 at 15:13 | comment | added | Elden Elmanto | you mean the index of a critical point of $f$? | |
| Aug 3, 2016 at 3:42 | history | asked | 54321user | CC BY-SA 3.0 |