Timeline for Hirzebruch-Riemann-Roch theorem for Riemann surfaces with boundary
Current License: CC BY-SA 3.0
5 events
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| Apr 4, 2019 at 11:27 | comment | added | Wakabaloola | @LiviuNicolaescu Does simplification occur when instead of boundaries we consider a Riemann surface with punctures? | |
| Oct 14, 2016 at 18:54 | comment | added | Liviu Nicolaescu | When you double the manifold you consider different boundary conditions on the two halves. The boundary contributions on the two sides the cancel each other. Let me also point out that the boundary contribution is metric dependent. It simplifies somewhat when the boundary is totally geodesic (say cylindrical metric near the boundary) but it still depends on the length of the boundary. | |
| Oct 14, 2016 at 15:05 | comment | added | Mtheorist | But it seems that a 'doubling trick' exists where one can glue two Riemann surfaces with boundaries to obtain the generalization I've mentioned, please see pages 811-813 of Mirror Symmetry by Hori et al., which are based on "Enumerative geometry of stable maps with Lagrangian boundary conditions and multiple covers of the disc" by Katz and Liu. Do these results agree with your paper? | |
| Oct 12, 2016 at 13:02 | history | edited | Liviu Nicolaescu | CC BY-SA 3.0 |
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| Oct 12, 2016 at 9:28 | history | answered | Liviu Nicolaescu | CC BY-SA 3.0 |