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
5 Pith papers cite this work. Polarity classification is still indexing.
5
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 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.
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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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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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).
- Gauge Symmetries, Contact Reduction, and Singular Field Theories