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Applied Topology Seminar

Monday, March 23, 2015 - 2:00pm

Iris Yoon

Penn Math

Location

University of Pennsylvania

DRL 4C8

Sperner’s lemma is a combinatorial result that is equivalent to the Brouwer fixed point theorem. We can consider a Sperner coloring as data parametrized by a simplex, and hence use sheaf theory to collate the data. We will first discuss constructs of cellular sheaves and cellular sheaf cohomology. Results from cellular cohomology generalize to analogous results in cellular sheaf cohomology. We will prove Sperner’s lemma using cellular sheaf cohomology and close with a discussion of other lemmas and theorems that we can revisit with the perspective of sheaf cohomology, such as Brouwer fixed point theorem and Helly’s theorem.