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СЕМИНАРЫ |
Семинар отдела геометрии и топологии МИАН «Геометрия, топология и математическая физика» (семинар С. П. Новикова)
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Kontsevich and Batalin–Vilkovisky classes in the ribbon graph complex A. Yu. Lazarev University of Bristol, Department of Mathematics |
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Аннотация: The ribbon graph complex computes the cohomology of moduli spaces of complex algebraic curves of all genera and with any number of marked points. An A-infinity algebra with an even invariant scalar product determines a cycle in the graph complex. Similarly, a differential contractible algebra with an odd invariant scalar product determines a cocycle in the graph complex. These constructions were originally sketched by Kontsevich over a decade ago but until now they have not been properly utilized. Using homologucal algebra and a finite dimensional analogue of the Batalin–Vilkovisky formalism in quantum field theory we give a conceptual reformulation of these constructions. We also construct infinite series of explicit nontrivial examples of these classes and compute their pairings in terms of asymptotic expansions of certain finite-dimensional integrals. |