# Bonn THDM 2013: Background

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

## [edit] 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*, 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 - and -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