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Maggie Miller, Zoom: Knotted handlebodies
Friday, January 21, 2022, 02:00pm - 03:00pm
Often, interesting knotting vanishes when allowed one extra dimension, e.g. knots in 3-space all become isotopic when included into 4-space. Hughes, Kim and I recently found a new counterexample to this principle: for g1, there exists a pair of 3-dimensional genus-g solids in the 4-sphere with the same boundary, and that are homeomorphic relative to their boundary, but do not become isotopic rel boundary even when their interiors are pushed into the 5-dimensional ball. This proves a conjecture of Budney and Gabai (who previously constructed 3-balls in the 4-sphere with the same boundary that are not isotopic rel boundary) for g1 in a very strong sense. In this talk, I'll describe some motivation from 3-dimensional topology and useful/weird facts about higher-dimensional knots (e.g. knotted surfaces in 4-manifolds), show how to construct interesting codimension-2 knotting in dimensions 4 and 5 (joint with Mark Hughes and Seungwon Kim), and talk about related open problems.
Location: Zoom

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