Some phenomena in tautological rings of manifolds
| Autor: | Oscar Randal-Williams |
|---|---|
| Přispěvatelé: | Randal-Williams, Oscar [0000-0002-7479-2878], Apollo - University of Cambridge Repository |
| Rok vydání: | 2018 |
| Předmět: |
Discrete mathematics
Pure mathematics Ring (mathematics) math.AT Rank (linear algebra) Mathematics::Commutative Algebra General Mathematics 010102 general mathematics General Physics and Astronomy Torus 01 natural sciences Upper and lower bounds Tautological line bundle Cohomology Mathematics::Algebraic Geometry 0103 physical sciences FOS: Mathematics Algebraic Topology (math.AT) 010307 mathematical physics Tautological one-form Krull dimension Mathematics - Algebraic Topology 0101 mathematics 55R40 57R22 Mathematics |
| DOI: | 10.17863/cam.26719 |
| 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. 21 pages; v2 29 pages, to appear in Selecta Mathematica |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|