Rob Kirby's Edinburgh Lectures
The visit of Rob Kirby (Berkeley) to Edinburgh in November 2012 was supported by Scheme 2 of the
London Mathematical Society.
Topological manifolds: their triangulations and smoothings
The 12 lectures were recorded on video by Carmen Rovi, with the links posted below.
Monday, November 5, 5PM, Room 5325, JCMB
Lecture #1 of Rob Kirby.
An extended introduction to Lectures #3-#12 on the triangulations of topological manifolds,
their existence and uniqueness,
and applications to topological
transversality, handlebodies, and the topological invariance of Whitehead torsion.
Wednesday, November 7, 3.30PM, Lecture Room C, JCMB
Lecture #2 of Rob Kirby The Arf-Rochlin invariant in manifold topology.
Abstract: I will discuss how the Arf invariant of a Z/2 enhancement of
a Z/2 intersection form is important in dimensions one (knot theory)
Slides. A historical talk at a colloquium-level.
Wednesday, November 7, 5.00PM, Lecture Room C, JCMB
Sir Michael Atiyah (Edinburgh) Chern classes for Real vector bundles.
Abstract: Mod 2 invariants, such as the Rochlin invariant, have links to
In my lecture I investigate a new version of Chern
classes that may shed light on these matters.
Lectures #3-12 of Rob Kirby follow on November 9,12,14,16,19,21,23,26,28,30,
at 5.00PM in Lecture Room A, JCMB.
Rob Kirby also gave a seminar on
Tuesday, November 27, 5.30PM, Lecture Room A, JCMB
Morse 2-functions and trisections of 4-manifolds
Abstract: In joint work with David Gay, we show existence
of Morse 2-functions (also known as broken
Lefschetz fibrations), and then existence and uniqueness
(up to stabilization) of trisections of 4-manifolds
(analogous to Heegaard splittings of 3-manifolds).
- Lecture 1. Introduction. Monday, November 5 Video
- Lecture 2. The Arf and Rochlin invariants. Wednesday, November 7 Video
- Lecture 3. Collars, the tangent bundle. Friday, November 9 Video
- Lecture 4. The torus trick and some of its applications. Monday, November 12 Video
- Lecture 5. The Schoenflies theorem. Wednesday, November 14
- Lecture 6. More torus trick. Friday, November 16
- Lecture 7. Concordance implies isotopy. Monday, November 19
- Lecture 8. The product structure theorem. Wednesday, November 21
- Lecture 9. Immersion theory and \pi_k(TOP/PL). Friday, November 23
- Lecture 10. Surgery and homotopy tori. Friday, November 26
- Lecture 11. Friday, November 28 Video
- Lecture 12. The finale. Friday, November 30 Video