Stratifications and equivariant cohomology of a spaces of upper-triangular square-zero matrices
Abstract/Contents
- Abstract
- Given an irreducible component X of the variety of square-zero upper-triangular matrices, a combinatorial formula developed by Rothbach gives a stratification of X into orbits of the Borel group. Specializing to the complex numbers and imposing a rank condition motivated by the Halperin-Carlsson conjecture on the free ranks of products of spheres, we consider a coarser stratification into orbits of the parabolic group. After illustrating the use of the singular value decomposition theorem to describe the topology of the strata, we then compute their equivariant cohomology. We conclude with applications to the Herzog-Kühl equations and their role in obstruction theory arguments motivated by the aforementioned conjecture.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2012 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Lee, Jonathan Wayne |
|---|---|
| Associated with | Stanford University, Department of Mathematics |
| Primary advisor | Carlsson, Gunnar |
| Thesis advisor | Carlsson, Gunnar |
| 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 | Jonathan Wayne Lee. |
|---|---|
| Note | Submitted to the Department of Mathematics. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2012. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2012 by Jonathan Wayne Lee
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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