Oberwolfach Surgery Seminar 2012: General information
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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
- Bundle theories DC
- Spivak normal fibration DC
- Normal invariants and surgery below the middle dimension DC
- Immersions, the Wall form and formations DC
- L-groups and Wall realisation DC
- The geometric surgery exact sequence DC
- The TOP surgery exact sequence TM
2.2 Algebraic surgery
- Structured chain complexes AR
- Symmetric and quadratic signature AR
- Algebraic surgery and L-groups via chain complexes AR
- Examples of Poincaré complexes MO SB CW AR
- Additive categories with chain duality and categories over complexes TM
- Generalized homology theories TM
- The normal complexes TM
2.3 Algebraic surgery versus geometric surgery
- The algebraic surgery exact sequence AR
- The topological block bundle obstruction TM
- The surgery obstruction TM
- The geometric and algebraic surgery exact sequences AR
- Examples and related developments AR
3 Schedule
3.1 Monday
- 9.00 - 10.00 Lecture 1
- 10.20 - 11.20 Lecture 2
- 11. 30 - 11.55 Exercise session 1
- 12.00 - 13.00 Lunch
- 13.00 - 14.30 Afternoon break
- 14.30 - 15.30 Lecture 3
- 15.50 - 16.50 Lecture 4
- 17.00 - 18.00 Exercise session 2
3.2 Tuesday
- 9.00 - 9.30 Special memorial lecture in honour of Profess Hirzebruch
- 9.30 - 10.30 Lecture 5
- 10.50 - 12.15 Lecture 6
- 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