Oberwolfach Surgery Seminar 2012: General information
From Manifold Atlas
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* [[:Category:Surgery|Surgery on the Manifold Atlas]] | * [[:Category:Surgery|Surgery on the Manifold Atlas]] | ||
* [http://www.dailymotion.com/playlist/x235tg_Carmen_Rovi_oberwolfach-surgery-theory/1#video=xr61y1| Videos of the Oberwolfach lectures] | * [http://www.dailymotion.com/playlist/x235tg_Carmen_Rovi_oberwolfach-surgery-theory/1#video=xr61y1| Videos of the Oberwolfach lectures] | ||
− | * [[User:Philipp Kuehl|Philipp Kühl's]] stenographic [[media: | + | * [[User:Philipp Kuehl|Philipp Kühl's]] stenographic [[media:OSS2012LectureNotes.pdf|lecture notes]]. |
== Prerequisites == | == 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. | 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. |
Latest revision as of 11:47, 6 August 2012
- Discussion
- Exercises
- Glossary
- Surgery on the Manifold Atlas
- Videos of the Oberwolfach lectures
- Philipp Kühl's stenographic lecture notes.
Contents |
[edit] 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].
[edit] 2 Program
[edit] 2.1 Geometric surgery
- Bundle theories DC: video mfo1
- Spivak normal fibration DC: video mfo2
- Normal invariants and surgery below the middle dimension DC : video mfo3
- Immersions, the Wall form and formations DC: video mfo4
- L-groups and Wall realisation DC video mfo5
- The geometric surgery exact sequence DC video mfo6
- The TOP surgery exact sequence TM video mfo7
[edit] 2.2 Algebraic surgery
- Structured chain complexes AR video mfo8
- Symmetric and quadratic signature AR video mfo9
- Algebraic surgery and L-groups via chain complexes AR video mfo10
- Additive categories with chain duality and categories over complexes TM video Part I-mfo11.1 video Part II-mfo11.2
- Generalized homology theories TM video Part I-mfo12.1
- The normal complexes TM
[edit] 2.3 Algebraic surgery versus geometric surgery
- The algebraic surgery exact sequence AR video mfo14
- The topological block bundle obstruction AR video mfo15
- The surgery obstruction TM & AR video Part I-mfo16.1
- The geometric and algebraic surgery exact sequences TM video mfo17
- Examples and related developments DC, TM, AR: video Part I Part II Part III
[edit] 2.4 Examples
- Examples of non-smoothable Poincaré complexes Martin Olbermann video, Steve Balady [video comming very soon], Christoph Winges video, AR video
[edit] 3 Schedule
[edit] 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
[edit] 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
[edit] 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)
[edit] 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
[edit] 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