Homotopical algebraic context over differential operators

in Journal of Homotopy and Related Structures (2019), 14(1), 293-347

Maurer-Cartan spaces of filtered L-infinity algebras

in Journal of Homotopy and Related Structures (2015)

We study several homotopical and geometric properties of Maurer- Cartan spaces for L-infinity algebras which are not nilpotent, but only filtered in a suitable way. Such algebras play a key role ... [more ▼]

We study several homotopical and geometric properties of Maurer- Cartan spaces for L-infinity algebras which are not nilpotent, but only filtered in a suitable way. Such algebras play a key role especially in the deformation theory of algebraic structures. In particular, we prove that the Maurer-Cartan simplicial set preserves fibrations and quasi-isomorphisms. Then we present an algebraic geometry viewpoint on Maurer-Cartan moduli sets, and we compute the tangent complex of the associated algebraic stack. [less ▲]

Reidemeister torsion for flat superconnections

in Journal of Homotopy and Related Structures (2014), 9(2), 579-606

We use higher parallel transport -- more precisely, the integration A-infinity-functor constructed in -to define Reidemeister torsion for flat superconnections. We conjecture a version of the Cheeger ... [more ▼]

We use higher parallel transport -- more precisely, the integration A-infinity-functor constructed in -to define Reidemeister torsion for flat superconnections. We conjecture a version of the Cheeger-Müller theorem, namely that the combinatorial Reidemeister torsion coincides with the analytic torsion defined by Mathai and Wu. [less ▲]

On level one cuspidal Bianchi modular forms

in Journal of Homotopy and Related Structures (2013), 16