Stable moduli of flat manifold bundles
Abstract/Contents
- Abstract
- Flat manifold bundles (i.e. manifold bundles with foliations transverse to the fibers) are classified by homotopy classes of maps to the classifying space of diffeomorphisms made discrete. In my thesis, I studied the homology of the classifying spaces of discrete diffeomorphisms for certain type of manifolds including surfaces, higher dimensional analogue of surfaces and disks with punctures. I established homological stability of discrete surface diffeomorphisms and discrete symplectic diffeomorphisms which was conjectured by Morita. To study the stable homology of these family of groups, I described an infinite loop space related to the Haefliger space whose homology is the same as group homology of discrete surface diffeomorphisms in the stable range which is the analogous of the Madsen-Weiss theorem for discrete surface diffeomorphisms. Similar theorems were proved for punctured 2-dimensional disk and higher dimensional analogue of surfaces. I utilized these new techniques of studying discrete diffeomorphism groups to obtain interesting applications to the characteristic classes of flat surface bundles and foliated bordism groups of codimension 2 foliations.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2015 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Nariman, Sam |
|---|---|
| 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 | Eliashberg, Y, 1946- |
| Thesis advisor | Mirzakhani, Maryam |
| Advisor | Cohen, Ralph L, 1952- |
| Advisor | Eliashberg, Y, 1946- |
| Advisor | Mirzakhani, Maryam |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Sam Nariman. |
|---|---|
| Note | Submitted to the Department of Mathematics. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2015. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2015 by Sam Nariman
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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