Oberwolfach Surgery Seminar 2012: General information
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=== Algebraic surgery === | === Algebraic surgery === | ||
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| − | + | <li>[[Oberwolfach Surgery Seminar 2012: Program#Structured chain complexes|Structured chain complexes]] [[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]] | |
| − | + | <li>[[Oberwolfach Surgery Seminar 2012: Program#Examples of Poincaré complexes|Examples of Poincaré complexes]] Speakers TBA | |
| − | + | <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#The normal complexes|The normal complexes]] [[User:Tibor Macko|TM]] | ||
| + | </ol> | ||
=== Algebraic surgery versus geometric surgery === | === Algebraic surgery versus geometric surgery === | ||
Revision as of 10:19, 31 May 2012
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
- 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 Speakers TBA
- 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 Daily Schedules
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
Tuesday, Thursday and Friday
- 9.00 - 10.00 Lecture 1
- 10.20 - 11.20 Lecture 2
- 11. 30 - 12.15 Exercise session 1
- 12.30 - 13.30 Lunch
- 13.30 - 15.00 Afternoon break
- 15.00 - 16.00 Lecture 3
- 16.20 - 17.20 Lecture 4
- 17.30 - 18.15 Exercise session 2
- 20:30 - 21:00 Manifold Atlas training session
Wednesday
- 9.00 - 10.00 Lecture 1
- 10.20 - 11.20 Lecture 2
- 11. 30 - 12.15 Exercise session 1
- 12.30 - 13.30 Lunch
- 13.30 - 18.30 Free afternoon
- 20.30 - 21.30 "Lecture 19" - Examples of Poincaré complexes
