Introduction to Whitney towers

Schneiderman, Rob

Winter Braids X (Pisa, 2020), Winter Braids Lecture Notes (2020), Exposé no. 4, 71 p.

These introductory notes on Whitney towers in 4-manifolds, as developed in collaboration with Jim Conant and Peter Teichner, are an expansion of three expository lectures given at the Winter Braids X conference February 2020 in Pisa, Italy. Topics presented include local manipulations of surfaces in $4$–space, fundamental definitions related to Whitney towers and their associated trees, geometric Jacobi identities, the classification of order $n$ twisted Whitney towers in the $4$–ball and higher-order Arf invariants, and low-order Whitney towers on $2$–spheres in $4$–manifolds and related invariants.

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