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A Geometric Definition of the Integral and Applications
Joshua Lackman
The standard definition of integration of differential forms is based on local coordinates and partitions of unity. This definition is mostly a formality and not used used in expli…
A Groupoid Construction of Functional Integrals: Brownian Motion and Some TQFTs
Joshua Lackman
We formalize Feynman's construction of the quantum mechanical path integral. To do this, we shift the emphasis in differential geometry from the tangent bundle onto the pair groupo…
A Groupoid Approach to the Riemann Integral (and Path Integral Quantization of the Poisson Sigma Model)
Joshua Lackman
We use groupoids and the van Est map to define Riemann sums on compact manifolds (with boundary), in a coordinate-free way. These Riemann sums converge to the usual integral after…
The van Est Map on Geometric Stacks
Joshua Lackman
We generalize the van Est map and isomorphism theorem in three ways, and we discuss conjectured connections with homotopy theory, including a proposal of a category which unifies d…