ATMW Classification of Manifolds (2013)

Speakers

Syllabus (Some addition/subtraction may be made in the topics)

Time-Table (First week)

Second week

References: (These form a very small portion of the literature on this topic but contains the original papers and books on the subject, more is available in the internet, however some of the books, which contain quite a bit of the materials to be covered, are highlighted with bold letters)

• BREDON G., Topology and Geometry, Springer 1993. This book introduces many of the tools needed for manifold surgery.
• BROWDER W., Surgery on simply connected manifolds, Springer-Verlag, 1972.
• DAVIS, J.F. and KIRK, P., Lectures Notes in Algebraic Topology, Department of Mathematics, Indiana University, Bloomington, IN 47405, E-mail address: jfdavis@indiana.edu, pkirk@indiana.edu
• GAULD David B., Differential Topology: An Introduction, Dover Publications, 2006.
• GUILLEMIN Victor and POLLACK Alan, Differential Topology, AMS, 2010.
• HIRSCH M.W., Differential Topology, Springer-Verlag, 1997.
• HUSEMULLER Dale, Fibre bundles, GTM-20, Springer, 1994.
• KERVAIRE M. and MILNOR J., *Groups of homotopy spheres-I*, Annals of Mathematics, Vol. 77 (1963), 504-537.
• KIRBY R.C. and SIEBENMANN L.C., Foundational Essays on the Topological manifolds, smoothing and triangulations, Annals of Mathematics Series No. 88, Princeton University Press (1977).
• KISTER, J.M., Microbundles and Fibre bundles, Annals of Mathematics, Second series Vol. 80, No. 1, 1964, pp. 190-199.
• KOSINSKI, A.A., Differential manifolds, Academic Press, 1993 and Dover publications, 2007.
• LÜCK Wolfgang , A basic introduction to Surgery theory, 2003.
• MILNOR J., ``Differential Topology'', Volume 3 of his collected papers, Amer. Math. Soc. 2007. Surgery theory was initiated by Milnor in the period 1956-1960 for the purpose of classifying smooth manifolds that are homotopy equivalent to a sphere of dimension \geq 5. In addition to published research articles, this volume contains four sets of notes for lectures he gave in this period; these lectures had remained in mimeographed form until their formal publication in this volume. They still provide excellent instruction in differential topology.
• MILNOR J., A procedure for killing homotopy groups of differentiable manifolds, Differential Geometry, Proc. Sympos. Pure Math. Vol. 3, pp. 39-55, Amer. Math. Soc. Providence, R. I., 1961.
• MILNOR J., Morse theory, (based on lecture notes by M. Spivak and R. Wells) Annals of Mathematical Studies No. 51, Princeton University Press, 1963.
• MILNOR J., Topology from the Differentiable Viewpoint, Univ. Pross of Virginia at Charlotesville, 1965.
• MILNOR J., Lectures on the h-cobordism theorem, (notes by L. Siebenmann and J. Sondow), Princeto Mathematical Notes, Princeton University Press, 1965.
• MILNOR J., Whitehead Torsion, Bull. Amer. Math. Soc. 72 (1966), 358-426.
• MILNOR J. and STASHEFF J., Characteristic classes, Annals of Mathematics Studies No. 76, Princeton University Press, 1974. This monograph is based on more succinct mimeographed notes by Milnor and Stasheff for lectures of Milnor given in 1959 and still available at <http://www.maths.ed.ac.uk/~aar/papers/milnorcc.pdf>.
• RANICKI A. A., Algebraic L-theory and topological manifolds, Cambridge Tracts in Math., vol. 102,Cambridge Univ. Press, Cambridge, 1992.
•  RANICKI A. A., Exact sequences in the algebraic theory of surgery, Princeton Univ. Press, Princeton, NJ, 1980. MR 82h:57027
• RANICKI A. A., Algebraic and Geometric Surgery, Oxford University Press, 2002.
• ROURKE R.C. and SANDERSON B.J., Introduction to Piecewise Linear Topology, Springer-Verlag, 1972.
• STEENROD Norman J. , Topology of Fibre bundles, Princeton, 1951; Landmarks in Mathematics and Physics; Princeton, 1999.
• WALL C.T.C., Surgery on Compact manifolds, 2nd Edition, Edited by Andrew Ranicki, 1998.
• WALLACE A.H., Differential Topology: First Steps, Dover Books on Mathematics, 2006.