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Universität Augsburg
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Universität Augsburg
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Dr. Maximilian Stegemeyer
University of Freiburg
spricht am
Montag, 21. Juli 2025
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16 Uhr s.t.
im
Raum 2004 (L1)
über das Thema:
| Abstract: |
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Properties of closed geodesics on Riemannian manifolds are a classical topic of mathematical research. The closed geodesics can be described as the critical points of the energy functional on the free loop space of the given manifold. Since string topology studies algebraic structures on the homology of free loop spaces, there is hope that string topology operations give new insight into closed geodesics.
In this talk we show how one can adapt a result by Hingston and Rademacher for closed geodesics on the sphere to real projective space. Since even-dimensional real projective space is not orientable the classical string topology operations are not defined and some extra care is required. We will show that a loop product and coproduct can be defined on the universal covering space of the free loop space of real projective space and that these new operations can be understood as extensions of the loop product and coproduct on the sphere. These operations can then be used to deduce a resonance theorem for real projective space. |
| Hierzu ergeht herzliche Einladung. |
| Zhen Gao |
Kaffee, Tee und Gebäck eine halbe Stunde vor Vortragsbeginn im Raum 2006 (L1).