103 citations · 908 across the 55 of their papers we have counts for
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Formal Abel-Jacobi maps
Domenico Fiorenza, Marco Manetti
We realize the infinitesimal Abel-Jacobi map as a morphism of formal deformation theories, realized as a morphism in the homotopy category of differential graded Lie algebras. The…
Boundary Conditions for Topological Quantum Field Theories, Anomalies and Projective Modular Functors
Domenico Fiorenza, Alessandro Valentino
We study boundary conditions for extended topological quantum field theories (TQFTs) and their relation to topological anomalies. We introduce the notion of TQFTs with moduli level…
Formality of Koszul brackets and deformations of holomorphic Poisson manifolds
Domenico Fiorenza, Marco Manetti
We show that if a generator of a differential Gerstenhaber algebra satisfies certain Cartan-type identities, then the corresponding Lie bracket is formal. Geometric examples includ…
Differential graded Lie algebras controlling infinitesimal deformations of coherent sheaves
Domenico Fiorenza, Donatella Iacono, Elena Martinengo
We use the Thom-Whitney construction to show that infinitesimal deformations of a coherent sheaf F are controlled by the differential graded Lie algebra of global sections of an ac…
Semicosimplicial DGLAs in deformation theory
Domenico Fiorenza, Marco Manetti, Elena Martinengo
We identify Cech cocycles in nonabelian (formal) group cohomology with Maurer-Cartan elements in a suitable L-infinity algebra. Applications to deformation theory are described.
L-infinity structures on mapping cones
Domenico Fiorenza, Marco Manetti
We show that the mapping cone of a morphism of differential graded Lie algebras can be canonically endowed with an -algebra structure which at the same t…