國立清華大學 數學系

Abstract: In general, a fiber product of smooth manifolds is not a manifold. In order to fix this incompleteness issue, we extend the category of smooth manifolds to a larger category in which one has homotopy fiber products. In the talk, following a framework of abstract homotopy theory, I will present a differential geometric way (using vector bundles and sections) to resolve the singular spaces raising from fiber products or zero sets of smooth functions. The talk is mainly based on a joint work in progress with Kai Behrend and Ping Xu.