47 citations · 357 across the 42 of their papers we have counts for
6 papers · 1 filter
Symplectic -algebras and string topology operations
Alastair Hamilton, Andrey Lazarev
In this paper we establish the existence of certain structures on the ordinary and equivariant homology of the free loop space on a manifold or, more generally, a formal Poincaré d…
Symplectic -algebras
Alastair Hamilton, Andrey Lazarev
In this paper we show that a strongly homotopy commutative (or -) algebra with an invariant inner product on its cohomology can be uniquely extended to a symplectic $C_\i…
Cohomology theories for homotopy algebras and noncommutative geometry
Alastair Hamilton, Andrey Lazarev
This paper builds a general framework in which to study cohomology theories of strongly homotopy algebras, namely and -algebras. This framework is ba…
Dual Feynman transform for modular operads
Joseph Chuang, Andrey Lazarev
We introduce and study the notion of a dual Feynman transform of a modular operad. This generalizes and gives a conceptual explanation of Kontsevich's dual construction producing g…
Graph homology: Koszul and Verdier duality
A. Lazarev, A. A. Voronov
We show that Verdier duality for certain sheaves on the moduli spaces of graphs associated to Koszul operads corresponds to Koszul duality of operads. This in particular gives a co…
Graph cohomology classes in the Batalin-Vilkovisky formalism
Alastair Hamilton, Andrey Lazarev
We give a conceptual formulation of Kontsevich's `dual construction' producing graph cohomology classes from a differential graded Frobenius algebra with an odd scalar product. Our…