Relations among characteristic classes of manifold bundles
Abstract/Contents
- Abstract
- We study a generalization of the tautological subring of the cohomology of the moduli space of Riemann surfaces to manifold bundles. The infinitely many "generalized Miller-Morita-Mumford classes" determine a map R from a free polynomial algebra to the cohomology of the classifying space of manifold bundles. In the case when M is the connected sum of g copies of the product of spheres (S^d times S^d), with d odd, we find numerous polynomials in the kernel of the map R and show that the image of R is a finitely generated ring. Some of the elements in the kernel do not depend on d. Our results contrast with the fact that the map R is an isomorphism in a range of cohomological degrees that grows linearly with g. This is known from theorems of Madsen-Weiss and Harer for the case of surfaces (d=1) and from the recent work of Soren Galatius and Oscar Randal-Williams in higher dimensions. For surfaces, the image of the map R coincides with the classical tautological ring, as introduced by Mumford.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2013 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Grigoriev, Ilya |
|---|---|
| Associated with | Stanford University, Department of Mathematics. |
| Primary advisor | Galatius, Søren, 1976- |
| Thesis advisor | Galatius, Søren, 1976- |
| Thesis advisor | Cohen, Ralph L, 1952- |
| Thesis advisor | Vakil, Ravi |
| Advisor | Cohen, Ralph L, 1952- |
| Advisor | Vakil, Ravi |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Ilya Grigoriev. |
|---|---|
| Note | Submitted to the Department of Mathematics. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2013. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2013 by Ilya Grigoriev
- License
- This work is licensed under a Creative Commons Attribution Share Alike 3.0 Unported license (CC BY-SA).
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