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 Events
University of Victoria
Wed 26 Feb 2020, 3:15pm
Topology and related seminars
ESB 4127
Isotopy in dimension 4
ESB 4127
Wed 26 Feb 2020, 3:15pm-10:00am

Abstract

 I will describe why the trivial knot S2-->S4 has non-unique spanning discs up to isotopy. This comes from a chain of deductions that include a description of the low-dimensional homotopy-groups of embeddings of S1 in S1xSn (for n>2), a group structure on the isotopy-classes of reducing discs of S1xDn, and the action of the diffeomorphism group Diff(S1xSn) on the embedding space Emb(S1, S1xSn).  Roughly speaking, these results say there is no direct translation from dimension 3 to 4, for the Hatcher-Ivanov theorems on spaces of incompressible surfaces. Or said another way, isotopy in dimension 4 is more closely analogous to isotopy in high dimensions. 
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