From gravity to string topology

DOI10.1007/s11005-023-01686-8arXiv2201.01122WikidataQ121074611 ScholiaQ121074611MaRDI QIDQ6113202

Sergey A. Merkulov

Publication date: 10 July 2023

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2201.01122

zbMATH Keywords

moduli spacesLie bialgebrasstring topologyproperads

Mathematics Subject Classification ID

Families, moduli of curves (algebraic) (14H10) String topology (55P50) Monoidal categories and operads (18Mxx)

Cites Work

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• The Frobenius properad is Koszul
• Maurer-Cartan elements and cyclic operads
• Higher genus Kashiwara-Vergne problems and the Goldman-Turaev Lie bialgebra
• Quantization of the Lie bialgebra of string topology
• Invariant functions on Lie groups and Hamiltonian flows of surface group representations
• Two-dimensional topological gravity and equivariant cohomology
• Combinatorial Lie bialgebras of curves on surfaces.
• Goldman-Turaev formality from the Knizhnik-Zamolodchikov connection
• The Goldman-Turaev Lie bialgebra in genus zero and the Kashiwara-Vergne problem
• Formal descriptions of Turaev's loop operations
• Homological algebra related to surfaces with boundary
• Operadic twisting -- with an application to Deligne's conjecture
• M. Kontsevich's graph complex and the Grothendieck-Teichmüller Lie algebra
• Equivariant operads, string topology, and Tate cohomology
• A dual version of the ribbon graph decomposition of moduli space
• Algebraic string operations
• INTERSECTIONS OF LOOPS IN TWO-DIMENSIONAL MANIFOLDS
• Deformation theory of Lie bialgebra properads
• A Koszul duality for props

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