Schedule for: 22w5065 - Topology in Dimension 4.5

A buffet dinner is served daily between 5:30pm and 7:30pm in Vistas Dining Room, top floor of the Sally Borden Building.

Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.

A brief introduction to BIRS with important logistical information, technology instruction, and opportunity for participants to ask questions.

Speakers: Anthony Conway, Seungwon Kim, Patrick Naylor, Arunima Ray.

Speakers: Anthony Conway, Seungwon Kim, Patrick Naylor, Arunima Ray.

Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

Meet in the PDC front desk for a guided tour of The Banff Centre campus.

Meet in foyer of TCPL to participate in the BIRS group photo. The photograph will be taken outdoors, so dress appropriately for the weather. Please don't be late, or you might not be in the official group photo!

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I will describe the eponymous groups in the topological category. When the boundary is nonempty, the complete computation is new and joint with Patrick Orson. Then I will do some subset of: (i) make comparisons with the smooth category; (ii) mention applications to isotopy of surfaces; (iii) discuss possible avenues for generalisation to 4-manifolds with non-trivial fundamental group.

This talk will focus on work in progress, joint with Mark Powell, on pseudoisotopy theory for topological 4-manifolds. The goal is to extend Quinn's theorem, that a pseudoisotopy of a simply-connected 4-manifold is topologically isotopic to an isotopy, to 4-manifolds with good fundamental groups, provided that the Hatcher-Wagoner obstructions vanish. A part of the project is to establish what the relevant analogue of Hatcher-Wagoner's higher-dimensional obstructions should be in dimension 4. The talk will aim to explain these notions, problems, and our results.

A buffet dinner is served daily between 5:30pm and 7:30pm in Vistas Dining Room, top floor of the Sally Borden Building.

Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.

Picture this!

Picture this!

Picture this!

Picture this!

Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

A relative trisection of a smooth 4-manifold with boundary induces an open book decomposition on the bounding 3-manifold, for which there is an algorithm to compute from the relative trisection diagram. In this talk I will discuss two works-in-progress which aim to better understand the relationship between trisections and open books. The first is to interpret a relative trisection as a commutative cubes of groups.  (joint with Jason Joseph and Patrick McFaddin); the second is obstructing destabilizations of relative trisections (joint with Thomas Kindred).

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Batson's conjecture is a non-orientable version of Milnor's conjecture, which states that the 4-ball genus of a torus knot T(p,q) is equal to 1/2(p-1)(q-1). Batson's conjecture states that the nonorientable 4-ball genus is equal to the pinch number of a torus knot, i.e. the number of a specific type of (nonorientable) band surgeries needed to obtain the unknot. The conjecture was recently proved to be false by Lobb. We will show that Lobb's counterexample fits into an infinite family of counterexamples.

A strong inversion of a knot K is an involution i of the 3-sphere that setwise fixes K and whose fixed set intersects K in exactly two points.The equivariant 4-genus of a (knot, inversion) pair (K, i) is defined to be the minimal genus of an embedded surface F in the 4-ball with boundary K and that is setwise fixed under some extension of i to an involution of the 4-ball. We give a new lower bound on the equivariant 4-genus in terms of the Blanchfield pairing, and discuss how this can be used to give many examples of knots with arbitrarily large equivariant 4-genus. In the process, we show that genus one strongly invertible knots with nontrivial Alexander polynomial are never equivariantly slice. This is joint work with Mark Powell.

A buffet dinner is served daily between 5:30pm and 7:30pm in Vistas Dining Room, top floor of the Sally Borden Building.

We will understand the Gromov Compactness Theorem by considering some examples.

Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.

Speakers: Dave Gabai, Michael Klug, Mark Powell, Rob Schneiderman.

Speakers: Dave Gabai, Michael Klug, Mark Powell, Rob Schneiderman.

Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

A buffet dinner is served daily between 5:30pm and 7:30pm in Vistas Dining Room, top floor of the Sally Borden Building.

Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.

Speakers: Ryan Budney, Daniel Hartman, Danica Kosanovic, Slava Krushkal, Tadayuki Watanabe.

Speakers: Ryan Budney, Daniel Hartman, Danica Kosanovic, Slava Krushkal, Tadayuki Watanabe.

Speakers: Ryan Budney, Daniel Hartman, Danica Kosanovic, Slava Krushkal, Tadayuki Watanabe.

Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

The Gluck twist of an embedded 2-sphere in the 4-sphere is a 4-manifold that is homeomorphic, but not obviously diffeomorphic to the 4-sphere. Despite considerable study, these homotopy spheres have resisted standardization except in special cases. In this talk, I will discuss some conditions that imply the double of a Gluck twist is standard, i.e., is diffeomorphic to the 4-sphere. This is based on joint work with Dave Gabai and Hannah Schwartz.

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We will discuss and compare two recent results of the author. First will be a family of homotopy 4-spheres constructed by Manolescu and Piccirillo by annulus twisting a ribbon disk. These we show are standard by visualizing the associated trace embedding by a Kirby diagram. To contrast this, we construct a family of exotic elliptic surfaces by annulus twisting an H-slice disk. This provides important evidence for the viability of the Manolescu-Piccirillo approach to disproving the smooth 4-dimensional Poincare conjecture by giving the first examples of their construction successfully producing exotic 4-manifolds.

We prove that the (2,1)-cable of the figure-eight knot is not smoothly slice by showing that its branched double cover bounds no equivariant homology ball. This answers a forty-year-old question posed by Kawauchi. (Joint with Sungkyung Kang, Abhishek Mallick, JungHwan Park, and Matthew Stoffregen.)

A buffet dinner is served daily between 5:30pm and 7:30pm in Vistas Dining Room, top floor of the Sally Borden Building.

Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.

I will describe a few different scanning arguments, allowing one to show the non-triviality of some implanted barbell diffeomorphisms, as elements of the homotopy groups of Diff($S^1 \times D^{n-1}$) for $n\ge 4$.

5-day workshop participants are welcome to use BIRS facilities (TCPL ) until 3 pm on Friday, although participants are still required to checkout of the guest rooms by 11AM.

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I will explain a new approach to settings with geometric dual spheres, which can not only classify isotopy classes of disks or spheres with such a dual, but also leads to some new insights into mapping class groups of 4-manifolds. This is joint work with Peter Teichner.