Algebraic filling inequalities and cohomological width
- For any continuous map f:X→Y and y∈Y the preimage f^{-1}(y) is a subset of X and we can consider the cohomological restriction homomorphism H^k(X;Z)→H^k(f^{-1}(y);Z). Gromov introduced the notion of cohomological width which is defined as min_{f:X→Y} max_{y∈Y} rk[H^k(X;Z)→H^k(f^{-1}(y);Z)]. We give new lower bounds for this quantity, when X is a product of projective spaces and Y is the real line and when X is a torus, an essential manifold with free abelian fundamental group or a product of higher-dimensional spheres and Y a manifold.
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| Author: | Meru Alagalingam |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-40833 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/4083 |
| Advisor: | Bernhard HankeORCiDGND |
| Type: | Doctoral Thesis |
| Language: | English |
| Date of Publication (online): | 2017/04/04 |
| Publishing Institution: | Universität Augsburg |
| Granting Institution: | Universität Augsburg, Mathematisch-Naturwissenschaftlich-Technische Fakultät |
| Date of final exam: | 2016/12/16 |
| Release Date: | 2017/04/04 |
| Tag: | cohomology; filling inequalities |
| GND-Keyword: | Isoperimetrische Ungleichung; Kohomologie |
| Institutes: | Mathematisch-Naturwissenschaftlich-Technische Fakultät |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik | |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Licence (German): |  Deutsches Urheberrecht |
