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**Next talk(s): TBA**

The mailing list for the topology seminar is: Topology-talks@lists.uvic.ca

Previous Talks 2017-2020 |
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**Speaker: **Ryan Budney

**Title: **Isotopy in dimension 4.

**Abstract:** I will describe why the trivial knot S^{2}-->S^{4} 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 S^{1} in S^{1}xS^{n}, a group structure on the reducing discs of S^{1}xD^{n}, and the action of Diff(S^{1}xS^{n}) on Emb(S^{1}, S^{1}xS^{n}).

**Date/Time: **Monday, January 20th. 2:30pm--3:30pm.

**Location: **DSB C130

**Speaker: **Ryan Budney

**Title: **3-balls in the 4-sphere and the Schoenflies problem

**Abstract: **I will describe a group structure on the isotopy-classes of smooth fiber bundles on S^{1}xD^{3}, fibering over the circle with fibre D^{3}, and show why the group of diffeomorphisms of S^{1}xD^{3} acts transitively on this group of isotopy-classes of fiberings. Via a Haefliger-style parameterized double-point method, we produce a not-finitely-generated subgroup of this group of fiberings. We describe an endomorphism of this group such that the 1-eigenvectors (i.e. the fixed points discarding the linear fibering) is the set of counter-examples to the smooth 4-dimensional Schoenflies problem.

**Date/Time: **Monday, December 16th. 10:30am -- 11:30am.

**Location: **DSB C114.

**Speaker**: Sam Churchill

**Title:** 3-manifolds algorithmically bound 4-manifolds part 1: the smooth case

**Abstract:** The terrain of manifold theory in dimension 4 is still being explored, with elements from low- and high-dimensional topology aiding the resolution of some problems. We explore a technique for constructing a bordism for a given smooth, closed, orientable 3-manifold M by applying the 3-manifold technique of constructing a geometric partition of the manifold. This partition provides handle attachment sites on the 4-manifold $M \times I$, which permits the construction of a 4-manifold with prescribed 3-manifold boundary. We pay close attention to how the handle attachment sites are found and defined, keeping an eye on the ultimate goal of converting this proof into an algorithm for triangulated 3- and 4-manifolds.

**Date/Time: **June 3rd, 3pm.

**Location: **David Strong Building C128

**Speaker**: Sam Churhill

**Title:** 3-manifolds algorithmically bound 4-manifolds part 2: adapting the smooth case to triangulations

**Abstract: **Adapting the proof from the previous talk to the realm of triangulated manifolds has its fair share of difficulties. We explore how to define and construct the triangulated analogues of the structures required for the smooth proof and present these constructions as algorithms.

**Date/Time:** June 4th, 1pm.

**Location:** Clearihue C110

**Speaker:** Ahmad Issa (U.T. Austin)

**Title:** Embedding Seifert fibered spaces in the 4-sphere

**Abstract:** Which 3-manifolds smoothly embed in the 4-sphere? This seemingly simple question turns out to be surprisingly subtle and difficult. In this talk, we restrict to the case of Seifert fibered 3-manifolds over an arbitrary oriented base surface F. Such a space M, with non-zero generalised Euler invariant, is determined by (F; e; r_1, ..., r_k) where e > 0 is an integer and r_1,...,r_k > 1 are rationals (here we've oriented M to bound a positive definite plumbing). For e >= k/2, we determine precisely which M pass a powerful obstruction to embedding based on Donaldson's theorem, and then attempt to either embed M or apply further obstructions in those cases. For e > k/2, this gives a complete determination of which such M embed. This is joint work with Duncan McCoy.

**Date/Time: **Friday December 1st, 10am.

**Location:** DSB C122

**Cascade Topology Seminar (59 ^{th}). Fall 2017.**

**Date/Time: **Weekend of October 20th, in Victoria BC.

Talks will begin at 10:30am on Saturday (four talks), and the meeting will end at noon on the Sunday (two talks).

**Speakers:**

- Geoffroy Horel (Paris 13)
- Keiichi Sakai (Shinshu U.)
- Gabriel Islambouli (U.Virginia)
- Jeff Meier (U. Georgia)
- Liam Watson (U. Sherbrooke)
- Tomasz Kaczynski (U. Sherbrooke)

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