Oberwolfach Surgery Seminar 2012: General information
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* 15.50 - 16.50 Lecture 4 | * 15.50 - 16.50 Lecture 4 | ||
* 17.00 - 18.00 Exercise session 2 | * 17.00 - 18.00 Exercise session 2 | ||
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Tuesday, Thursday and Friday | Tuesday, Thursday and Friday | ||
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* 16.20 - 17.20 Lecture 4 | * 16.20 - 17.20 Lecture 4 | ||
* 17.30 - 18.15 Exercise session 2 | * 17.30 - 18.15 Exercise session 2 | ||
+ | * 20:30 - 21:00 Manifold Atlas training session | ||
Wednesday | Wednesday | ||
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* 13.30 - 18.30 Free afternoon | * 13.30 - 18.30 Free afternoon | ||
* 20.30 - 21.30 "Lecture 19" - Examples of Poincaré complexes | * 20.30 - 21.30 "Lecture 19" - Examples of Poincaré complexes | ||
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== References == | == References == | ||
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[[Category:Oberwolfach Surgery Seminar 2012]] | [[Category:Oberwolfach Surgery Seminar 2012]] |
Revision as of 17:54, 28 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