Bonn THDM 2013: Background

Latest revision as of 02:34, 26 August 2013

• Schedule
• Program
• Exercises

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] and the first six chapters of the book [Husemoller1994]. 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], [Crowley2010], [Kühl&Macko&Mole2011], [Lück&Reich2005], [Bartels&Lück&Reich2008], [Bartels&Lück2012].

There is also a reading guide for surgery theory for topological manifolds available at the discussion page of the TSO-at-MFO 2012

References

• [Bartels&Lück&Reich2008] A. Bartels, W. Lück and H. Reich, On the Farrell-Jones Conjecture and its applications, Journal of Topology 1 (2008), 57–86. MR2365652 (2008m:19001) Zbl 1141.19002
• [Bartels&Lück2012] A. Bartels and W. Lück, The Borel conjecture for hyperbolic and CAT(0)-groups., Ann. of Math. (2) 175 (2012), 631–689. MR2993750 Zbl 06025000
• [Crowley2010] D. Crowley, The smooth structure set of $* [[Bonn THDM 2013: Exercises|Exercises]] * [[Bonn THDM 2013: Glossary|Glossary]] * [[Bonn THDM 2013: Program|Program]] * [[Bonn THDM 2013: Schedule|Schedule]] * [[:Category:Surgery|Surgery on the Manifold Atlas]] <!--* [http://www.dailymotion.com/playlist/x235tg_Carmen_Rovi_oberwolfach-surgery-theory/1#video=xr61y1| Videos of the Oberwolfach lectures] * [[User:Philipp Kuehl|Philipp Kühl's]] stenographic [[media:OSS2012LectureNotes.pdf|lecture notes]].--> == Prerequisites == The prerequisites for the seminar are knowledge of the basics of differential and algebraic topology, meaning: manifolds, Poincaré duality, bundles, cobordism, transversality, generalized homology and cohomology and homotopy groups. Participants should be familiar with the concepts and ideas covered in the first 7 chapters of the book {{citeD|Ranicki2002}}. In addition participants should be familiar with the basics of spectra in stable homotopy theory. A good reference here is {{citeD|Hatcher2002|Section 4.F}}. The main references for the material covered in the seminar are {{citeD|Lück2001}} and {{citeD|Kühl&Macko&Mole2011}}. There is also a reading guide for surgery theory for topological manifolds available at the [http://www.map.mpim-bonn.mpg.de/Oberwolfach_Surgery_Seminar_2012:_Discussion discussion page of the TSO-at-MFO 2012] [[Category:Bonn THDM 2013]]S^p\times S^q$, Geom. Dedicata 148 (2010), 15–33. MR2721618 (2012a:57041) Zbl 1207.57043
• [Hatcher2002] A. Hatcher, Algebraic topology, Cambridge University Press, 2002. MR1867354 (2002k:55001) Zbl 1044.55001
• [Husemoller1994] D. Husemoller, Fibre bundles, 3rd ed., Springer-Verlag, 1994. MR1249482 (94k:55001) Zbl 0794.55001
• [Kühl&Macko&Mole2011] P. Kuehl, T. Macko and A. Mole, The total surgery obstruction revisited, (2011). Available at the arXiv:1104.5092.
• [Lück&Reich2005] W. Lück and H. Reich, The Baum-Connes and the Farrell-Jones conjectures in $K$- and $L$-theory, Handbook of K-theory. Vol. 1, 2, 703–842, Springer, Berlin, 2005. MR2181833 (2006k:19012) Zbl 1120.19001
• [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
• [Ranicki2002] A. Ranicki, Algebraic and geometric surgery, The Clarendon Press Oxford University Press, Oxford, 2002. MR2061749 (2005e:57075) Zbl 1003.57001