Oberwolfach Surgery Seminar 2012: General information
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Participants should be familiar with the ideas covered in the first 7 chapters of the book {{citeD|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}}. | Participants should be familiar with the ideas covered in the first 7 chapters of the book {{citeD|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 {{citeD|Ranicki1979}}, {{citeD|Ranicki1992}, {{citeD|Kühl&Macko&Mole2011}} and {{citeD|Wall1999}. | + | The main references for the material covered in the seminar are {{citeD|Ranicki1979}}, {{citeD|Ranicki1992}}, {{citeD|Kühl&Macko&Mole2011}} and {{citeD|Wall1999}. |
== Schedule == | == Schedule == |
Revision as of 16:55, 17 April 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 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 {{citeD|Wall1999}.
2 Schedule
2.1 Geometric surgery
- Bundle theories DC
- Spivak normal fibration DC
- Normal invariants and surgery below the middle dimension DC
- L-groups of rings with involution DC
- Surgery obstructions 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
- Algebraic bordism categories 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 TM
- The topological block bundle obstruction TM
- The surgery obstruction AR
- The geometric and algebraic surgery exact sequences AR
- Examples and related developments AR