Poincaré duality holds for Rabinowitz Floer homology and cohomology as graded Frobenius algebras, extending to open-closed TQFT duality, with applications to cotangent bundles and loop spaces.
String Topology
6 Pith papers cite this work. Polarity classification is still indexing.
6
Pith papers citing it
abstract
Consider two families of closed oriented curves in a d-manifold. At each point of intersecction of a curve of one family with a curve of the other family, form a new closed curve by going around the first curve and then going around the second. Typically, an i-dimensional family and a j-dimensional family will produce an (i+j-d+2)-dimensional family. Our purpose is to describe mathematical structure behind such interactions.
representative citing papers
The Lagrangian capacity of every convex or concave toric symplectic domain equals its diagonal, settling the Cieliebak–Mohnke ellipsoid conjecture and two related conjectures.
The paper constructs functional flat bundles with rational connections on infinite-dimensional manifolds to generalize Hamiltonian and renormalization group evolution in QFT, concluding spacetime notions emerge as spectral sets of functional differential operators.
Reduced loop homology is introduced so the loop product and coproduct form a unital infinitesimal anti-symmetric bialgebra satisfying a modified Sullivan relation, established via reduced symplectic homology on Weinstein manifolds.
Singular (gauge) theories with a global scaling symmetry can be reduced to an equivalent frictional theory, and the order of constraint-imposition and scale-reduction does not matter.
Under a non-nilpotency condition in free loop space homology with respect to the Chas-Sullivan product, the number of simple Reeb orbits on star-shaped hypersurfaces grows at least like T/log(T).
citing papers explorer
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Poincar\'e duality for loop spaces
Poincaré duality holds for Rabinowitz Floer homology and cohomology as graded Frobenius algebras, extending to open-closed TQFT duality, with applications to cotangent bundles and loop spaces.
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Lagrangian capacity and chain level string topology
The Lagrangian capacity of every convex or concave toric symplectic domain equals its diagonal, settling the Cieliebak–Mohnke ellipsoid conjecture and two related conjectures.
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Flat Bundles on Function Manifolds and Evolution Equations in Quantum Field Theories
The paper constructs functional flat bundles with rational connections on infinite-dimensional manifolds to generalize Hamiltonian and renormalization group evolution in QFT, concluding spacetime notions emerge as spectral sets of functional differential operators.
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Reduced symplectic homology and string topology
Reduced loop homology is introduced so the loop product and coproduct form a unital infinitesimal anti-symmetric bialgebra satisfying a modified Sullivan relation, established via reduced symplectic homology on Weinstein manifolds.
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Gauge Symmetries, Contact Reduction, and Singular Field Theories
Singular (gauge) theories with a global scaling symmetry can be reduced to an equivalent frictional theory, and the order of constraint-imposition and scale-reduction does not matter.
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On the growth rate of Reeb orbit on star-shaped hypersurfaces
Under a non-nilpotency condition in free loop space homology with respect to the Chas-Sullivan product, the number of simple Reeb orbits on star-shaped hypersurfaces grows at least like T/log(T).