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VIGRE seminar, spring 2000: Topics in Combinatorics and Topology

Laura Anderson
Students enrolled
Crystal Hoyt, Roel Morales (undergraduate mathematics students); Stephen Shauger, Conrad Yang (graduate mathematics students)
This seminar approached topology via spaces constructed combinatorially (e.g., simplicial complexes). This approach allowed us to sidestep most of the content of the usual introductory topology course and start working with spaces without developing extensive theory. The main thrust was the relationship between the topology and combinatorics of spaces with combinatorial constructions. Topics included: general and piecewise linear topology, Euler characteristic, Mobius function, f-vectors, topology of partially ordered sets, shellings and their generalizations.