Homotopy fiber product of manifolds

Abstract: A main motivation of developing derived differential geometry is to deal with singularities arising from zero loci or intersections of submanifolds. Both zero loci and intersections can be considered as fiber products of manifolds which may not be manifolds. Thus, we extend the category of differentiable manifolds to a larger category in which one has "homotopy fiber products". In this talk, I would like to show a construction, using vector bundles, sections and connections, of homotopy fiber products of manifolds and explain structures behind the construction. The talk is mainly based on a joint work with Kai Behrend and Ping Xu.

mathematical physicsdifferential geometrysymplectic geometry

Audience: researchers in the topic

( paper )

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