Combinatorial Differential Topology and Geometry
نویسنده
چکیده
A variety of questions in combinatorics lead one to the task of analyzing the topology of a simplicial complex, or a more general cell complex. However, there are few general techniques to aid in this investigation. On the other hand, the subjects of differential topology and geometry are devoted to precisely this sort of problem, except that the topological spaces in question are smooth manifolds. In this paper we show how two standard techniques from the study of smooth manifolds, Morse theory and Bochner’s method, can be adapted to aid in the investigation of combinatorial spaces.
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