Topology Seminar (Introductory Talk): The Arf invariant is seen in all dimensions (part 1)

Seminar | April 27 | 2:10-3 p.m. | 740 Evans Hall

Rob Kirby, UC Berkeley

Department of Mathematics

This is a historical talk, beginning with Arf's defnition in 1938. It was overlooked until Pontrjagin mistakenly claimed that the 4th homotopy group of the 2-sphere was 0 and eventually found his error and the Arf invariant. Then Rohlin missed a factor of 2 and this can be seen as the Arf invariant. Then it appears in Kervaire's 10-manifold without a smooth structure. Then as the simplest knot invariant. And finally it is the Z/2 that appears in the triangulations work of me and Siebenmann. This will spread over the two hours.

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