University of Cambridge > Talks.cam > Junior Geometry Seminar > Topological Incarnations of the Arf invariant

Topological Incarnations of the Arf invariant

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  • UserDanica Kosanovic (MPIM Bonn)
  • ClockFriday 02 June 2017, 15:00-16:00
  • HouseMR5.

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The Arf invariant is an invariant of nonsingular quadratic forms over F_2. Although seemingly too simple, it appears in several contexts in geometric topology (as a concordance invariant of knots, in the Freedman-Kirby generalisation of Rokhlin theorem, as Kervaire invariant), which also hint its relation to the theory of 4-dimensional manifolds. In this introductory talk I will give an overview of spin and Pin^{\pm}-structures and associated cobordism rings in low dimensions, present a geometric interpretation of the Arf invariant and relate it to the Rokhlin invariant of homology 3-spheres.

This talk is part of the Junior Geometry Seminar series.

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