Relations among characteristic classes of manifold bundles
| Autor: | Grigoriev, Ilya |
|---|---|
| Rok vydání: | 2013 |
| Předmět: | |
| Zdroj: | Geom. Topol. 21 (2017) 2015-2048 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.2140/gt.2017.21.2015 |
| Popis: | We study relations among characteristic classes of smooth manifold bundles with highly-connected fibers. For bundles with fiber the connected sum of $g$ copies of a product of spheres $S^d \times S^d$ and an odd $d$, we find numerous algebraic relations among the so-called "generalized Miller-Morita-Mumford classes". For all $g > 1$, we show that these infinitely many classes are algebraically generated by a finite subset. Our results contrast with the fact that there are no algebraic relations among these classes in a range of cohomological degrees that grows linearly with $g$, according to recent homological stability results. In the case of surface bundles ($d=1$), our approach recovers some previously known results about the structure of the classical "tautological ring", as introduced by Mumford, using only the tools of algebraic topology. Comment: Accepted version. Numerous minor imporvements. 35 pages, 1 figure |
| Databáze: | arXiv |
| Externí odkaz: |
|