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String Topology
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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.
Forward citations
Cited by 14 Pith papers
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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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Resonances and string point invertibility for compact rank one symmetric spaces
For compact rank one symmetric spaces, string point invertibility over a field of characteristic p holds exactly when p equals the Euler characteristic, and the same condition yields uniform resonance bounds on critic...
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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 spe...
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Quartic BV structures in supercategories and modified necklace Lie bialgebras
The augmented necklace Lie bialgebra, whose bracket and cobracket insert rather than remove involution pairs of arrows, is claimed to satisfy the IBL axioms and is witnessed by quartic Poisson/BV structures on represe...
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Parametric Gromov width of Liouville domains
Introduces parametric Gromov width and proves Floer and string-topology upper bounds constraining parameterized symplectic embeddings beyond classical Gromov width.
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Chain level Koszul duality between the Gravity and Hypercommutative operads
A chain model for the hypercommutative operad is constructed and shown to be the Koszul dual of a chain model for the gravity operad.
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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 Weinst...
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Dimer Models and Hochschild Cohomology
For zigzag consistent dimers on a torus, the Hochschild cohomology of the Jacobi algebra and the compactly supported Hochschild cohomology of the matrix factorization category are computed in explicit combinatorial te...
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String topology operations under Chen's iterated integrals and homotopy transfer
Chen iterated integrals plus homotopy transfer intertwine the involutive Lie bialgebra of S1-equivariant string topology with the IBL operations on the dual cyclic bar complex of a harmonic subspace.
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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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Bordered Legendrian Rational Symplectic Field Theory
Bordered LSFT algebras are defined for half-knots, and a pushout theorem recovers Ng's commutative LSFT algebra of the whole Legendrian knot.
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Deformation and quantization of the Loday-Quillen-Tsygan isomorphism for Calabi-Yau categories
For Koszul Calabi-Yau algebras, the Loday-Quillen-Tsygan isomorphism deforms to a co-Poisson bialgebra isomorphism and quantizes to a Hopf algebra isomorphism, induced from the Lie bialgebra on the cyclic homology of ...
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Loop Patterns Formed by Cellular Automata
A probabilistic cellular automaton with overlapping-tile templates and noise injection can evolve stable, non-touching loop patterns on 2D grids under fixed boundaries.
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