Some phenomena in tautological rings of manifolds
| Autor: | Randal-Williams, Oscar |
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| Rok vydání: | 2016 |
| Předmět: | |
| Zdroj: | Selecta Math. (N.S.) 24 (2018), no. 4, 3835-3873 |
| Druh dokumentu: | Working Paper |
| Popis: | We prove several basic ring-theoretic results about tautological rings of manifolds W, that is, the rings of generalised Miller--Morita--Mumford classes for fibre bundles with fibre W. Firstly we provide conditions on the rational cohomology of W which ensure that its tautological ring is finitely-generated, and we show that these conditions cannot be completely relaxed by giving an example of a tautological ring which fails to be finitely-generated in quite a strong sense. Secondly, we provide conditions on torus actions on W which ensure that the rank of the torus gives a lower bound for the Krull dimension of the tautological ring of W. Lastly, we give extensive computations in the tautological rings of CP^2 and S^2 x S^2. Comment: 21 pages; v2 29 pages, to appear in Selecta Mathematica |
| Databáze: | arXiv |
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