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Unknotted gropes and Whitney towers in 4-space

Banff International Research Station for Mathematical Innovation and Discovery

Gropes and Whitney towers are primary tools for studying 4-dimensional topology. As an effort to understand gropes and Whitney towers via the structure of their complements, we introduce notions of unknotted gropes/Whitney towers in 4-space. This is motivated by Freeman's result that an embedded 2-sphere in 4-space is topologically unknotted if its complement has infinite cyclic fundamental group. As an application, we establish grope and Whitney tower bi-filtrations of knots in 3-space by taking a slice of unknotted gropes/Whitney towers. Using the amenable signature theorem by Cha, which is based on the work of Cha and Orr, we prove that these bi-filtrations have rich structures. This is joint work with Jae Choon Cha.

Mathematics; Manifolds and cell complexes; Differential geometry; Low dimensional topology

video/mp4

Author affiliation: Konkuk University

2016-08-26

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/58992

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/