Loop Products and Closed Geodesics
By Mark Goresky, Nancy Hingston. 2007
87 citations recorded by the source corpus.
We show the Chas-Sullivan product (on the homology of the free loop space of a Riemannian manifold) is related to the Morse index of its closed geodesics. We construct related products in the cohomology of the free loop space and of the based loop space, and show they are nontrivial.
Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/876d1b8f3a6d738e364cde4555aed93206afe433
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In Applied Mathematics
In Geometry and Topology
- Basak Z. Gurel
- V. Ginzburg
- A. Oancea
- Kai Cieliebak
- P. Seidel
- M. Abouzaid
- Alexander F. Ritter
- Frederick J. Bourgeois III
In Mathematical Physics
- V. Ginzburg
- A. Oancea
- Basak Z. Gurel
- Kai Cieliebak
- Alexander F. Ritter
- Frederick J. Bourgeois III
- Mark McLean
- P. Seidel
Citations in the corpus
- Hochschild homology of structured algebras (2011, unknown): “1] and is expected to be related to the Goresky-Hingston product on the cohomology of the free loop space on a manifold [22].”
- Lusternik–Schnirelmann theory and closed Reeb orbits (2016, background): “oned in the introduction that under reasonable assumptions (co)homology operations (such as Dor the pair-of-pants product) vanish in the local homology of an isolated orbit; cf. [GG10, Prop. 5.3] and [GoHi]. 2.3.2. Equivariant Morse–Bott Floer homology. We will now consider another case of localizat”
- Symplectic homology and the Eilenberg-Steenrod axioms (2015, background): “Following Seidel, there is another coproduct of degree 1 − n on SH ∗ (V ) obtained as a secondary operation in view of the fact that the natural coproduct given by counting pairs of pants with one input and two outputs vanishes, see also [40] for a generalization and [47] for a topological version o”