Oberwolfach Surgery Seminar 2012: General information
From Manifold Atlas
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* [[Oberwolfach Surgery Seminar 2012: Glossary|Glossary]] | * [[Oberwolfach Surgery Seminar 2012: Glossary|Glossary]] | ||
* [[: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] | ||
| + | * [[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. | ||
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== Program == | == Program == | ||
===Geometric surgery=== | ===Geometric surgery=== | ||
| − | + | <ol> | |
| − | + | <li>[[Oberwolfach Surgery Seminar 2012: Program#Bundle theories|Bundle theories]] [[User:Diarmuid Crowley|DC]]: [http://www.dailymotion.com/video/xr61y1_mfo1_tech video mfo1] | |
| − | + | ||
| − | + | <li>[[Oberwolfach Surgery Seminar 2012: Program#Spivak normal fibration|Spivak normal fibration]] [[User:Diarmuid Crowley|DC]]: [http://www.dailymotion.com/video/xr6og1_mfo2_tech video mfo2] | |
| − | + | ||
| − | + | <li>[[Oberwolfach Surgery Seminar 2012: Program#Normal invariants and surgery below the middle dimension|Normal invariants and surgery below the middle dimension]] [[User:Diarmuid Crowley|DC]] : [http://www.dailymotion.com/video/xr6edc_mfo3_tech video mfo3] | |
| − | + | ||
| + | <li>[[Oberwolfach Surgery Seminar 2012: Program#L-groups of rings with involution|Immersions, the Wall form and formations]] [[User:Diarmuid Crowley|DC]]: [http://www.dailymotion.com/video/xr6f0d_mfo4_tech video mfo4] | ||
| + | |||
| + | <li>[[Oberwolfach Surgery Seminar 2012: Program#Surgery obstructions|L-groups and Wall realisation]] [[User:Diarmuid Crowley|DC]] [http://www.dailymotion.com/video/xr787c_mfo5_tech video mfo5] | ||
| + | |||
| + | <li>[[Oberwolfach Surgery Seminar 2012: Program#The geometric surgery exact sequence|The geometric surgery exact sequence]] [[User:Diarmuid Crowley|DC]] [http://www.dailymotion.com/video/xr7881_mfo6_tech video mfo6] | ||
| + | |||
| + | <li>[[Oberwolfach Surgery Seminar 2012: Program#The TOP surgery exact sequence|The TOP surgery exact sequence]] [[User:Tibor Macko|TM]] [http://www.dailymotion.com/video/xr7mlu_mfo7_tech video mfo7] | ||
| + | </ol> | ||
=== Algebraic surgery === | === Algebraic surgery === | ||
<ol start="8"> | <ol start="8"> | ||
| − | <li>[[Oberwolfach Surgery Seminar 2012: Program#Structured chain complexes|Structured chain complexes]] [[User:Ranicki|AR]] | + | <li>[[Oberwolfach Surgery Seminar 2012: Program#Structured chain complexes|Structured chain complexes]] [[User:Ranicki|AR]] [http://www.dailymotion.com/video/xr7mn5_mfo8_tech video mfo8] |
| + | |||
<li>[[Oberwolfach Surgery Seminar 2012: Program#Symmetric and quadratic signatures|Symmetric and quadratic signature]] [[User:Ranicki|AR]] | <li>[[Oberwolfach Surgery Seminar 2012: Program#Symmetric and quadratic signatures|Symmetric and quadratic signature]] [[User:Ranicki|AR]] | ||
| − | <li>[[Oberwolfach Surgery Seminar 2012: Program#Algebraic surgery and L-groups via chain complexes|Algebraic surgery and L-groups via chain complexes]] [[User:Ranicki|AR]] | + | [http://www.dailymotion.com/video/xr7zqv_mfo9_tech video mfo9] |
| − | <li>[[Oberwolfach Surgery Seminar 2012: Program#Additive categories with chain duality and categories over complexes|Additive categories with chain duality and categories over complexes]] [[User:Tibor Macko|TM]] | + | |
| − | <li>[[Oberwolfach Surgery Seminar 2012: Program#Generalized homology theories|Generalized homology theories]] [[User:Tibor Macko|TM]] | + | <li>[[Oberwolfach Surgery Seminar 2012: Program#Algebraic surgery and L-groups via chain complexes|Algebraic surgery and L-groups via chain complexes]] [[User:Ranicki|AR]] [http://www.dailymotion.com/video/xr7zrd_mfo10_tech video mfo10] |
| + | |||
| + | <li>[[Oberwolfach Surgery Seminar 2012: Program#Additive categories with chain duality and categories over complexes|Additive categories with chain duality and categories over complexes]] [[User:Tibor Macko|TM]] [http://www.dailymotion.com/video/xrdisb_mfo11-1_tech video Part I-mfo11.1] [http://www.dailymotion.com/video/xreag3_mfo11-2_tech video Part II-mfo11.2] | ||
| + | |||
| + | <li>[[Oberwolfach Surgery Seminar 2012: Program#Generalized homology theories|Generalized homology theories]] [[User:Tibor Macko|TM]] [http://www.dailymotion.com/video/xreig3_mfo12-1_tech video Part I-mfo12.1] | ||
| + | |||
<li>[[Oberwolfach Surgery Seminar 2012: Program#The normal complexes|The normal complexes]] [[User:Tibor Macko|TM]] | <li>[[Oberwolfach Surgery Seminar 2012: Program#The normal complexes|The normal complexes]] [[User:Tibor Macko|TM]] | ||
</ol> | </ol> | ||
| Line 31: | Line 47: | ||
=== Algebraic surgery versus geometric surgery === | === Algebraic surgery versus geometric surgery === | ||
<ol start="14"> | <ol start="14"> | ||
| − | <li>[[Oberwolfach Surgery Seminar 2012: Program#The algebraic surgery exact sequence|The algebraic surgery exact sequence]] [[User:Ranicki|AR]] | + | <li>[[Oberwolfach Surgery Seminar 2012: Program#The algebraic surgery exact sequence|The algebraic surgery exact sequence]] [[User:Ranicki|AR]] [http://www.dailymotion.com/video/xrefbk_mfo14_tech video mfo14] |
| − | <li>[[Oberwolfach Surgery Seminar 2012: Program#The topological block bundle obstruction|The topological block bundle obstruction]] [[User: | + | |
| − | <li>[[Oberwolfach Surgery Seminar 2012: Program#The surgery obstruction|The surgery obstruction]] [[User:Tibor Macko|TM]] | + | <li>[[Oberwolfach Surgery Seminar 2012: Program#The topological block bundle obstruction|The topological block bundle obstruction]] [[User:Ranicki|AR]] [http://www.dailymotion.com/video/xrcsbt_mfo15_tech video mfo15] |
| − | <li>[[Oberwolfach Surgery Seminar 2012: Program#The geometric and algebraic surgery exact sequences|The geometric and algebraic surgery exact sequences]] [[User: | + | |
| − | <li>[[Oberwolfach Surgery Seminar 2012: Program#Examples and related developments|Examples and related developments]] [[User:Diarmuid Crowley|DC]], [[User:Tibor Macko|TM]], [[User:Ranicki|AR]] | + | <li>[[Oberwolfach Surgery Seminar 2012: Program#The surgery obstruction|The surgery obstruction]] [[User:Tibor Macko|TM & AR]] [http://www.dailymotion.com/video/xrcsb0_mfo16-1_tech video Part I-mfo16.1] |
| + | |||
| + | <li>[[Oberwolfach Surgery Seminar 2012: Program#The geometric and algebraic surgery exact sequences|The geometric and algebraic surgery exact sequences]] [[User: Tibor Macko|TM]] [http://www.dailymotion.com/video/xrcscv_mfo17_tech video mfo17] | ||
| + | |||
| + | <li>[[Oberwolfach Surgery Seminar 2012: Program#Examples and related developments|Examples and related developments]] [[User:Diarmuid Crowley|DC]], [[User:Tibor Macko|TM]], [[User:Ranicki|AR]]: [http://www.dailymotion.com/video/xrcset_mfo18-1_tech video Part I] [http://www.dailymotion.com/video/xrdbvl_mfo18-2_tech Part II] [http://www.dailymotion.com/video/xrdbwz_mfo18-3_tech Part III] | ||
</ol> | </ol> | ||
| + | |||
=== Examples=== | === Examples=== | ||
<ol start="19"> | <ol start="19"> | ||
| − | <li>[[Oberwolfach Surgery Seminar 2012: Program#Examples of non-smoothable Poincaré complexes|Examples of non-smoothable Poincaré complexes]] [[User:Martin Olbermann|Martin Olbermann]], [[User:Steve Balady|Steve Balady]], [[User:Winges|Christoph Winges]], [[User:Ranicki|AR]]</li> | + | <li>[[Oberwolfach Surgery Seminar 2012: Program#Examples of non-smoothable Poincaré complexes|Examples of non-smoothable Poincaré complexes]] [[User:Martin Olbermann|Martin Olbermann]] [http://www.dailymotion.com/video/xrei05_mfo19-1_tech video], [[User:Steve Balady|Steve Balady]] [video comming very soon], [[User:Winges|Christoph Winges]] [http://www.dailymotion.com/video/xredjx_mfo19-3_tech video], [[User:Ranicki|AR]] [http://www.dailymotion.com/video/xrcr6e_mfo20_tech video]</li> |
</ol> | </ol> | ||
| + | |||
== Schedule == | == Schedule == | ||
=== Monday === | === Monday === | ||
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* 16.20 - 17.20 Lecture 14 (AR) | * 16.20 - 17.20 Lecture 14 (AR) | ||
* 17.30 - 18.15 Exercise session 6 | * 17.30 - 18.15 Exercise session 6 | ||
| − | * 20.00 - 20.30 [http://web.math.princeton.edu/conference/browder2012/media/Day2/Talk%205%20-%20William%20Browder/williambrowder. | + | * 20.00 - 20.30 [http://web.math.princeton.edu/conference/browder2012/media/Day2/Talk%205%20-%20William%20Browder/williambrowder.m4v Film of Browder's retirement lecture, May 2012, Princeton] |
* 21.00 - 22.00 Piano concert by Marek Kaluba and Carmen Rovi | * 21.00 - 22.00 Piano concert by Marek Kaluba and Carmen Rovi | ||
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 |
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: 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
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
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
2.4 Examples
- 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
