A Lower Bound for Immersions of Real Grassmannians
Public Deposited- Last Modified
- February 26, 2019
- Creator
-
Lochbaum, Marshall
- Affiliation: College of Arts and Sciences, Department of Mathematics
- Abstract
- The cohomology of the real Grassmann and flag manifolds is discussed at length, making use of Stiefel-Whitney classes. It is shown that the tangent bundle of the Grassmannian splits into line bundles over the flag manifold. Additionally, it is found that the cohomology of the flag manifold is exactly the polynomial algebra โค(subscript 2)[๐(subscript 1),...,๐(subscript ๐)], for one-dimensional classes ๐(subscript ๐), modulo the relation โ(subscript ๐)(1 + ๐(subscript ๐))=1. Using facts about this ring to compute the dimension of the Stiefel-Whitney class of the normal bundle to the Grassmannian, we find a lower bound for immersions of certain real Grassmannians. In particular, G(subscript ๐)(โ(superscript ๐+๐)) with ๐โค2(superscript ๐ )โค๐ and ๐+๐โค2(superscript 1+๐ ) cannot be immersed in dimension less than ๐(2(superscript ๐ +1)-1).
- Date of publication
- autumn 2014
- Keyword
- DOI
- Resource type
- Rights statement
- In Copyright
- Note
- Funding: None
- Advisor
- Sawon, Justin
- Degree
- Bachelor of Science
- Honors level
- Highest Honors
- Degree granting institution
- University of North Carolina at Chapel Hill
- Extent
- 22 p.
Relations
- Parents:
This work has no parents.