56 citations · 370 across the 46 of their papers we have counts for
14 papers · 1 filter
Vector Fields and Flows on Subcartesian Spaces
Yael Karshon, Eugene Lerman
This paper is part of a series of papers on differential geometry of -ringed spaces. In this paper, we study vector fields and their flows on a class of singular spaces.…
Differential forms on -ringed spaces
Eugene Lerman
We construct a complex of differential forms on a local -ringed space. The two main classes of spaces we have in mind are differential spaces in the sense of Sikorski and…
Left-invariant vector fields on a Lie 2-group
Eugene Lerman
A Lie 2-group is a category internal to the category of Lie groups. Consequently it is a monoidal category and a Lie groupoid. The Lie groupoid structure on gives rise to t…
Lie 2-algebras of vector fields
Daniel Berwick-Evans, Eugene Lerman
We show that the category of vector fields on a geometric stack has the structure of a Lie 2-algebra. This proves a conjecture of R.~Hepworth. The construction uses a Lie groupoid…
Parallel Transport on Principal Bundles over Stacks
Brian Collier, Eugene Lerman, Seth Wolbert
In this paper we introduce a notion of parallel transport for principal bundles with connections over differentiable stacks. We show that principal bundles with connections over st…
Equivariant differential characters and symplectic reduction
Eugene Lerman, Anton Malkin
We describe equivariant differential characters (classifying equivariant circle bundles with connections), their prequantization, and reduction.