Bonn THDM 2013: Background
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| − | The prerequisites for the Summer School are knowledge of the basics of differential and algebraic topology, meaning: manifolds, Poincaré duality, bundles, cobordism, transversality, | + | The prerequisites for the Summer School are knowledge of the basics of differential and algebraic topology, meaning: manifolds, Poincaré duality, group rings, bundles and principle bundles, cobordism, transversality, homotopy groups and generalized (co)homology theories. |
Participants should be familiar with the concepts and ideas covered in the first 7 chapters of the book {{citeD|Ranicki2002}}. In addition participants should be familiar with the basics of spectra in stable homotopy theory. A good reference here is {{cite|Hatcher2002|Section 4.F}}. | Participants should be familiar with the concepts and ideas covered in the first 7 chapters of the book {{citeD|Ranicki2002}}. In addition participants should be familiar with the basics of spectra in stable homotopy theory. A good reference here is {{cite|Hatcher2002|Section 4.F}}. | ||
Revision as of 15:11, 20 June 2013
The prerequisites for the Summer School are knowledge of the basics of differential and algebraic topology, meaning: manifolds, Poincaré duality, group rings, bundles and principle bundles, cobordism, transversality, homotopy groups and generalized (co)homology theories.
Participants should be familiar with the concepts and ideas covered in the first 7 chapters of the book [Ranicki2002]. 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 [Lück2001] and [Kühl&Macko&Mole2011].
There is also a reading guide for surgery theory for topological manifolds available at the discussion page of the TSO-at-MFO 2012
References
- [Hatcher2002] A. Hatcher, Algebraic topology, Cambridge University Press, 2002. MR1867354 (2002k:55001) Zbl 1044.55001
- [Kühl&Macko&Mole2011] P. Kuehl, T. Macko and A. Mole, The total surgery obstruction revisited, (2011). Available at the arXiv:1104.5092.
- [Lück2001] W. Lück, A basic introduction to surgery theory, 9 (2001), 1–224. Available from the author's homepage. MR1937016 (2004a:57041) Zbl 1045.57020
