On free loop spaces of toric spaces
A. Bahri, M. Bendersky, S. Gitler, F. R. Cohen

TL;DR
This paper investigates the growth patterns of the rational homology of free loop spaces in toric spaces, linking fan structures to exponential growth and implications for periodic geodesics.
Contribution
It establishes a connection between the fan structure of toric manifolds and the exponential growth of their free loop space homology.
Findings
Hilbert-Poincaré series growth is exponential for certain toric manifolds
Fan structure determines the homological growth rate
Applications to existence of infinitely many periodic geodesics
Abstract
Growth of the Hilbert-Poincar\"e series for the rational homology of the free loop space of a toric space is addressed. In case the toric space is a manifold, the structure of the fan dictates whether the Hilbert-Poincar\"e series has exponential growth. Applications are made to the existence of infinitely many geometrically distinct periodic geodesics.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Combinatorial Mathematics · Geometric and Algebraic Topology · Topological and Geometric Data Analysis
