Partial quasi-morphisms and quasi-states on cotangent bundles, and symplectic homogenization

By Alexandra Monzner, Nicolas Vichery, F. Zapolsky. 2011

72 citations recorded by the source corpus.

For a closed connected manifold N, we construct a family of functions on the Hamiltonian group G of the cotangent bundle T^*N, and a family of functions on the space of smooth functions with compact support on T^*N. These satisfy properties analogous to those of partial quasi-morphisms and quasi-states of Entov and Polterovich. The families are parametrized by the first real cohomology of N. In the case N=T^n the family of functions on G coincides with Viterbo's symplectic homogenization operator. These functions have applications to the algebraic and geometric structure of G, to Aubry-Mather theory, to restrictions on Poisson brackets, and to symplectic rigidity.

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/32007bf2b05f369aedbae83aba2979bee2358a2f

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In Geometry and Topology

1. E. Shelukhin
2. A. Kislev
3. Sobhan Seyfaddini
4. Vincent Humilière
5. R. Leclercq
6. A. Sorrentino
7. F. Zapolsky

In Mathematical Physics

1. E. Shelukhin
2. A. Kislev
3. Sobhan Seyfaddini
4. Vincent Humilière
5. R. Leclercq
6. A. Sorrentino
7. F. Zapolsky

In Statistical and Nonlinear Physics

1. Sobhan Seyfaddini
2. R. Leclercq
3. Vincent Humilière
4. E. Shelukhin
5. A. Sorrentino

Citations in the corpus

• Coisotropic rigidity and $C^{0}$-symplectic geometry (2013, methodology): “otangent bundles. We briefly outline below the construction of these invariants via Lagrangian Floer homology and collect their main properties in this situation. We refer to Monzner– Vichery–Zapolsky [18] which gives a very nice exposition of the theory. Let Lbe a smooth compact manifold, L 0 denote”
• On the Homogenization of the Hamilton-Jacobi Equation (2019, methodology): “used by different communities with different meanings; in this work, we refer to our result as a “Homogenization result for the Hamilton-Jacobi equation”, in the same spirit as it is done in [9], [33], [27], etc. In the remaing part of this introduction, in order to present our main result, we need to”
• Bounds on spectral norms and barcodes (2018, background): “ology by Viterbo in [118] by means of generating functions, then in Floer theory by Schwarz [97], and Oh [84, 85], and in Lagrangian Floer theory by Leclercq [64] and Leclercq-Zapolsky [65] (see also [44, 77, 81]). We refer to [65] for a review of the literature. In terms of Lagrangian (resp. Hamilt”