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math.CT2000
Infinitesimal aspects of the Laplace operator
Anders Kock
In the context of synthetic differential geometry, we study the Laplace operator an a Riemannian manifold. The main new aspect is a neighbourhood of the diagonal, smaller than the…
math.CT2000
Volume form as volume of infinitesimal simplices
Anders Kock
In the context of Synthetic Differential Geometry, we describe the square volume of a ``second-infinitesimal simplex'', in terms of square-distance between its vertices. The square…
math.CT2000
Algebra of Principal Fibre Bundles, and Connections
Anders Kock
We put together some of the efforts by several people of making aspects of fibre bundle theory into algebra. The initiator of these efforts was Charles Ehresmann, who put the notio…