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Bruno Vallette

  1. Givental group action on Topological Field Theories and homotopy Batalin--Vilkovisky algebras.

    Чт, 12/08/2011 - 15:01 — SomNambul
    Authors: Sergey Shadrin, Vladimir Dotsenko, Bruno Vallette
    Subjects: Quantum Algebra
    Abstract

    In this paper, we initiate the study of the Givental group action on
    Cohomological Field Theories in terms of homotopical algebra. More precisely,
    we show that the stabilisers of Topological Field Theories in genus 0
    (respectively in genera 0 and 1) are in one-to-one correspondence with
    commutative homotopy Batalin--Vilkovisky algebras (respectively wheeled
    commutative homotopy BV-algebras).

  2. Homotopy Batalin-Vilkovisky algebras.

    Чт, 03/31/2011 - 15:01 — SomNambul
    Authors: Imma Galvez-Carrillo, Andy Tonks, Bruno Vallette
    Subjects: Quantum Algebra
    Abstract

    This paper provides an explicit cofibrant resolution of the operad encoding
    Batalin-Vilkovisky algebras. Thus it defines the notion of homotopy
    Batalin-Vilkovisky algebras with the required homotopy properties.

    To define this resolution we extend the theory of Koszul duality to operads
    and properads that are defind by quadratic and linear relations. The operad
    encoding Batalin-Vilkovisky algebras is shown to be Koszul in this sense. This
    allows us to prove a Poincare-Birkhoff-Witt Theorem for such an operad and to
    give an explicit small quasi-free resolution for it.

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