Events

Ryan Budney 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. hide