Hopf invariants, rational homotopy theory, and physical integrals.
Event details
| Date | 02.02.2016 |
| Hour | 10:15 › 11:30 |
| Speaker | Dev Sinha |
| Location |
MA110
|
| Category | Conferences - Seminars |
We discuss a basic question in algebraic topology: given two maps f,g : X —> Y, how can we tell whether or not they are homotopic? One condition is that f and g should pull back cohomology in the same way. But even when X is a sphere, this is far from sufficient. In relatively recent work, Ben Walter and I resolve this question when X is a sphere and Y is simply connected, rationally (that is, up to then multiplying f and g by some non-zero integer). We do so by giving explicit integrals, generalizing Whitehead’s integral formula for the Hopf invariant, which has been cited regularly in the physics literature. These integrals are a concrete manifestation of Koszul duality. These integrals are also similar to integrals developed by Cattaneo and Mnev in the context of Chern-Simons theory. We speculate on the connection, as well as potential connection with L_\infty models for rational homotopy theory.
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Practical information
- Informed public
- Free
Organizer
- Magdalena Kedziorek