Oberwolfach Surgery Seminar 2012: General information

• Glossary
• Surgery on the Manifold Atlas

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 A. Hatcher, Algebraic topology, Cambridge University Press, 2002. MR1867354 (2002k:55001) Zbl 1044.55001.

The main references for the material covered in the seminar are [Ranicki1979], [Ranicki1992], [Kühl&Macko&Mole2011] and [Wall1999].

2 Schedule

2.1 Geometric surgery

1. Bundle theories DC
2. Spivak normal fibration DC
3. Normal invariants and surgery below the middle dimension DC
4. L-groups of rings with involution DC
5. Surgery obstructions DC
6. The geometric surgery exact sequence DC
7. The TOP surgery exact sequence TM

2.2 Algebraic surgery

1. Structured chain complexes AR
2. Symmetric and quadratic signature AR
3. Algebraic surgery and L-groups via chain complexes AR
4. Examples of Poincaré complexes Speakers TBA
5. Algebraic bordism categories and categories over complexes TM
6. Generalized homology theories TM
7. The normal complexes TM

2.3 Algebraic surgery versus geometric surgery

1. The algebraic surgery exact sequence TM
2. The topological block bundle obstruction TM
3. The surgery obstruction AR
4. The geometric and algebraic surgery exact sequences AR
5. Examples and related developments AR