Oberwolfach Surgery Seminar 2012: General information

• Discussion
• Exercises
• Glossary
• Surgery on the Manifold Atlas
• Videos of the Oberwolfach lectures
• Philipp Kühl's stenographic lecture notes.

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: video mfo1
2. Spivak normal fibration DC: video mfo2
3. Normal invariants and surgery below the middle dimension DC : video mfo3
4. Immersions, the Wall form and formations DC: video mfo4
5. L-groups and Wall realisation DC video mfo5
6. The geometric surgery exact sequence DC video mfo6
7. The TOP surgery exact sequence TM video mfo7

2.2 Algebraic surgery

8. Structured chain complexes AR video mfo8
9. Symmetric and quadratic signature AR video mfo9
10. Algebraic surgery and L-groups via chain complexes AR video mfo10
11. Additive categories with chain duality and categories over complexes TM video Part I-mfo11.1 video Part II-mfo11.2
12. Generalized homology theories TM video Part I-mfo12.1
13. The normal complexes TM

2.3 Algebraic surgery versus geometric surgery

14. The algebraic surgery exact sequence AR video mfo14
15. The topological block bundle obstruction AR video mfo15
16. The surgery obstruction TM & AR video Part I-mfo16.1
17. The geometric and algebraic surgery exact sequences TM video mfo17
18. Examples and related developments DC, TM, AR: video Part I Part II Part III

2.4 Examples

19. Examples of non-smoothable Poincaré complexes Martin Olbermann video, Steve Balady [video comming very soon], Christoph Winges video, AR video

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 (TM)
• 16.20 - 17.20 Lecture 8 (AR)
• 17.30 - 18.15 Exercise session 3

3.3 Wednesday

• 9.00 - 10.00 Lecture 9 (AR)
• 10.20 - 11.20 Lecture 10 (AR)
• 11. 30 - 12.15 Exercise session 4
• 12.30 - 13.30 Lunch
• 13.30 - 18.30 Free afternoon
• 20.00 - 22.00 Lecture 19 - Examples of Poincaré complexes (Martin Olbermann, Steve Balady, Christoph Winges, AR)

3.4 Thursday

• 9.00 - 10.00 Lecture 11 (TM)
• 10.20 - 11.20 Lecture 12 (TM)
• 11.30 - 12.15 Exercise session 5
• 12.30 - 13.30 Lunch
• 13.30 - 15.00 Afternoon break
• 15.00 - 16.00 Lecture 13 (TM)
• 16.20 - 17.20 Lecture 14 (AR)
• 17.30 - 18.15 Exercise session 6
• 20.00 - 20.30 Film of Browder's retirement lecture, May 2012, Princeton
• 21.00 - 22.00 Piano concert by Marek Kaluba and Carmen Rovi

3.5 Friday

• 9.00 - 10.00 Lecture 15 (AR)
• 10.20 - 11.20 Lecture 16 (TM)
• 11.30 - 12.15 Exercise session 7
• 12.30 - 13.30 Lunch
• 13.30 - 15.00 Afternoon break
• 15.00 - 16.00 Lecture 17 (TM)
• 16.20 - 17.35 Lecture 18 (DC, TM, AR)
• 17.40 - 18.25 Exercise session 8