Oberwolfach Surgery Seminar 2012: General information

• Exercises
• Glossary
• Surgery on the Manifold Atlas

1 Prerequisites

The prerequisites for the seminar are a solid knowledge of the basics of differential and algebraic topology, meaning: manifolds, Poincaré duality, bundles, cobordism, transversality, generalized homology and cohomology, homotopy groups.

Participants should be familiar with the ideas covered in the first 7 chapters of the book [Ranicki2002]. However material from sections 2.2., 4.2, 5.4, 7.3 will be covered during the seminar. In addition participants should be familiar with the basics of spectra in stable homotopy theory. A good reference here is [Hatcher2002, Section 4.F].

The main references for the material covered in the seminar are [Ranicki1979], [Ranicki1992], [Kühl&Macko&Mole2011] and [Wall1999].

2 Program

2.1 Geometric surgery

1. Bundle theories DC
2. Spivak normal fibration DC
3. Normal invariants and surgery below the middle dimension DC
4. Immersions, the Wall form and formations DC
5. L-groups and Wall realisation DC
6. The geometric surgery exact sequence DC
7. The TOP surgery exact sequence TM

2.2 Algebraic surgery

8. Structured chain complexes AR
9. Symmetric and quadratic signature AR
10. Algebraic surgery and L-groups via chain complexes AR
11. Examples of Poincaré complexes MO SB CW AR
12. Additive categories with chain duality and categories over complexes TM
13. Generalized homology theories TM
14. The normal complexes TM

2.3 Algebraic surgery versus geometric surgery

15. The algebraic surgery exact sequence AR
16. The topological block bundle obstruction TM
17. The surgery obstruction TM
18. The geometric and algebraic surgery exact sequences AR
19. Examples and related developments AR

3 Schedule

3.1 Monday

• 9.00 - 10.00 Lecture 1 (DC)
• 10.20 - 11.20 Lecture 2 (DC)
• 11. 30 - 11.55 Exercise session 1
• 12.00 - 13.00 Lunch
• 13.00 - 14.30 Afternoon break
• 14.30 - 15.30 Lecture 3 (DC)
• 15.50 - 16.50 Lecture 4 (DC)
• 17.00 - 18.00 Exercise session 2

3.2 Tuesday

• 9.00 - 9.30 Special memorial lecture in honour of Hirzebruch (AR)
• 9.30 - 10.30 Lecture 5 (DC)
• 10.50 - 12.15 Lecture 6 (DC)
• 12.15 - 12.30 Photo
• 12.30 - 13.30 Lunch
• 13.30 - 15.00 Afternoon break
• 15.00 - 16.00 Lecture 7
• 16.20 - 17.20 Lecture 8
• 17.30 - 18.15 Exercise session 3

3.3 Wednesday

• 9.00 - 10.00 Lecture 9
• 10.20 - 11.20 Lecture 10
• 11. 30 - 12.15 Exercise session 4
• 12.30 - 13.30 Lunch
• 13.30 - 18.30 Free afternoon
• 20.00 - 22.00 Lecture 11 - Examples of Poincaré complexes

3.4 Thursday

• 9.00 - 10.00 Lecture 12
• 10.20 - 11.20 Lecture 13
• 11.30 - 12.15 Exercise session 5
• 12.30 - 13.30 Lunch
• 13.30 - 15.00 Afternoon break
• 15.00 - 16.00 Lecture 14
• 16.20 - 17.20 Lecture 15
• 17.30 - 18.15 Exercise session 6
• 20.00 - 20.30 Film of Browder's retirement lecture
• 21.00 - 22.00 Piano concert by Marek Kaluba and Carmen Rovi

3.5 Friday

• 9.00 - 10.00 Lecture 16
• 10.20 - 11.20 Lecture 17
• 11. 30 - 12.15 Exercise session 7
• 12.30 - 13.30 Lunch
• 13.30 - 15.00 Afternoon break
• 15.00 - 16.00 Lecture 18
• 16.20 - 17.20 Lecture 19
• 17.30 - 18.15 Exercise session 8