Tautological characteristic classes II: the Witt class
| Autor: | Dymara, Jan, Januszkiewicz, Tadeusz |
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| Rok vydání: | 2024 |
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| Zdroj: | Math. Ann. 390 (2024), no. 3, 4463-4496 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s00208-024-02851-7 |
| Popis: | Let $K$ be an arbitrary infinite field. The cohomology group $H^2(SL(2,K), H_2\,SL(2,K))$ contains the class of the universal central extension. When studying representations of fundamental groups of surfaces in $SL(2,K)$ it is useful to have classes stable under deformations (Fenchel--Nielsen twists) of representations. We identify the maximal quotient of the universal class which is stable under twists as the Witt class of Nekovar. The Milnor--Wood inequality asserts that an $SL(2,{\bf R})$-bundle over a surface of genus $g$ admits a flat structure if and only if its Euler number is $\leq (g-1)$. We establish an analog of this inequality, and a saturation result for the Witt class. The result is sharp for the field of rationals, but not sharp in general. Comment: 1 Figure |
| Databáze: | arXiv |
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