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Revisiting the Arf invariant

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Speaker: 
Danica Kosanović
Affiliation: 
MPIM
Date: 
Mon, 2018-12-17 16:30 - 18:00
Location: 
MPIM Lecture Hall
Parent event: 
MPIM Topology Seminar

The Arf invariant is an invariant of non-singular quadratic forms over Z/2. Although seemingly too simple, it appears in several contexts in geometric topology (as a concordance invariant of knots, in the Freedman-Kirby generalization of Rokhlin theorem, as Kervaire invariant). In the first part of the talk I will introduce Arf invariants and spin structures. I will then show how in low dimensions they relate and make explicit the 4-dimensional nature of the Arf invariant for knots.

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