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.
@article{WBLN_2020__7__A4_0, author = {Rob Schneiderman}, title = {Introduction to {Whitney} towers}, journal = {Winter Braids Lecture Notes}, note = {talk:4}, pages = {1--71}, publisher = {Winter Braids School}, volume = {7}, year = {2020}, doi = {10.5802/wbln.36}, language = {en}, url = {https://proceedings.centre-mersenne.org/articles/10.5802/wbln.36/} }
Rob Schneiderman. Introduction to Whitney towers. Winter Braids Lecture Notes, Volume 7 (2020), Talk no. 4, 71 p. doi : 10.5802/wbln.36. https://proceedings.centre-mersenne.org/articles/10.5802/wbln.36/
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