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Formality theorem for differential graded manifolds

Πότε 06/06/2018
από 14:30 έως 15:30
Που A11
Παριστάμενοι Professor Matthieu Stienon, Penn State University, U.S.A.
Προσθήκη γεγονότος στο ημερολόγιο vCal
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“Formality theorem for differential graded manifolds”

Professor Matthieu Stienon, Penn State University, U.S.A.

Περίληψη:The Atiyah class of a dg manifold (M, Q) is the obstruction to the existence of an affine connection that is compatible with the homological vector field Q. The Todd class of dg manifolds extends both the classical Todd class of complex manifolds and the Duflo element of Lie theory.
Using Kontsevich’s famous formality theorem, Liao, Xu and I established a formality theorem for smooth dg manifolds: given any finite-dimensional dg manifold (M, Q), there exists an L8 quasi-isomorphism of dglas from an appropriate space of polyvector fields endowed with the Schouten bracket [´, ´] and the differential [Q, ´] to an appropriate space of polydifferential operators endowed with the Gerstenhaber bracket [[´, ´]] and the differential [[m+Q, ´]], whose
first Taylor coefficient:
a) is equal to the composition of the action of the square root of the Todd class of the dg manifold (M, Q) on the space of polyvector fields with the Hochschild–Kostant–Rosenberg map and
b) preserves the associative algebra structures on the level of cohomology

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