ATMW Classification of Manifolds (2013)
Venue:  NEHU, Shillong 
Dates:  17th to 26th Jun 
Convener(s)  Speakers, Syllabus and Time table  Applicants/Participants 
Name  Himadri Kumar Mukerjee 
Mailing Address 
Department of Mathematics,

Classification of manifolds is a very old and natural problem in topology. Classification of one and two dimensional manifolds up to diffeomorphism has been done more than a century ago. The basic technique underlying these works have been “surgery” (cutting and gluing). The same technique have been extended to attack classification problems of manifolds of dimension 3, 4 and > 4. In dimension 3 and 4 one could achieve only a very little owing to the limitations of algebraic topological tools developed in the late twentieth century. Bigger success in these dimensions had to rely heavily on geometry and analysis. I dimension > 4 complete classification is ruled out owing to unsolvability of word problem, consequently classification of manifolds within a homotopy type have been tried. Surgery theory had a great success in this domain as exemplified by works of Milnor, Kervaire, Browder, Novikov, Wall, Kirby, Siebenmann, and numerous other very renowned mathematicians.
The purpose of the ATM workshop/conference on surgery theory and classification of manifolds would be to expose the participants to the basic techniques of surgery and related works leading to the surgery exact sequence for the classification of manifolds of dimension > 4 within a homotopy type, together with many applications, in a condensed and yet lucid fashion, help participants in digesting the topics through tutorials, and to familiarize them with the current problems through the papers to be presented in the applications and conference section.
Speakers
Sr.  Name  Affiliation 
1  James F. Davis  Indiana University Bloomington, USA 
2  L.C. Siebenmann  Université de Parissud, Centre d’Orsay, France 
3  Parameswaran Sankaran  IMSC, Chennai, India 
4  S. K. Roushon  TIFR, Mumbai, India 
5  C.S. Aravinda  TIFR, Bangalore, India 
6  Goutam Mukherjee  Indian Statistical Institute, Kolkata, India 
7  Samik Basu  Rankrishna Mission Vivekananda University, Howrah, India 
8  Himadri Kumar Mukerjee  NEHU, Shillong, India 
9  S.S. Khare  Dept. of Maths, NEHU, Shillong 
Syllabus (Some addition/subtraction may be made in the topics)
Topic 
Lectures 
Detailed Syllabus 
Topic 1 (TNB)  1 (75 minutes)  Tangent bundle, immersion and embedding, normal bundle. 
Topic 2 (FR)  1 (75 m)  Homotopy classification of vector bundles, framing of a normal bundle, parallelizable and sparallelizable manifolds. 
Topic 3 (HM)  1 (75 m)  Handle decompositions and Morse theory 
Topic 4 (HS)  1 (75 m)  hcobordism and scobordism theorems 
Topic 5 (SBMD)  2 (75 m each)  Surgery below the middle dimension 
Topic 6 (SMD0)  2 (75 m each)  Surgery below the middle dimension 
Topic 7 (SMD2)  2 (75 m each)  Surgery in the middle dimension of a 4kmanifold 
Topic 8 (ALTS)  2 (75 m each)  Surgery in the middle dimension of a (4k+2)manifold 
Topic 9 (SES)  2 (75 m each)  Lgroups and the algebraic theory of surgery 
Topic 10 (ES)  1 (75 m)  Surgery exact sequence 
Topic 11 (CSSAM)  1 (75 m)  Exotic spheres 
Topic 12 (CLSH)  1 (75 m)  Classifying homotopy complex projective spaces and homotopy lens spaces 
Topic 13 (BNC)  1 (75 m)  The Borel and Novikov Conjectures 
Topic 14 (STM)  1 (75 m)  Splitting theorems in manifold theory 
Topic 15 (FJC1)  1 (75 m)  The FarrellJones Conjectures 
Topic 16 (FJC2))  1 (75 m)  Applications of the FarrellJones Conjecture 
Topic 17 (TUPS)  12 (75 m)  Tutorials and problem sessions 
Topic 18 (CFTK)  12 (435 m total)  Conference talks 
TimeTable (First week)
Day, Date & Time 
Monday 17062013 
Tuesday 18062013 
Wednesday 19062013 
Thursday 20062013 
Friday 
Saturday 22062013 
9.00  10.15  TNB  HS  SMD01  SMD22  SES1  CSSAM 
10.15  10.30  Tea/Coffee  
10.30  11.45  FR  SBMD1  SMD01  ALTS1  SES 2  TUPS 
11.45  12.00  Tea/Coffee  
12.00  13.15  HM  SBMD2  SBMD1  ALTS2  ES  TUPS 
13.15  14.45  LUNCH  
14.45  16.00  TUPS  TUPS  TUPS  TUPS  TUPS  Break 
16.00  16.15  Tea/Coffee  Break  
16.15  17.30  TUPS  TUPS  TUPS  TUPS  TUPS  Break 
17.30  SNACKS  Break 
Second week
Day, Date & Time 
Monday 24062013 
Tuesday 25062013 
Wednesday 26062013 
9.00  10.00  CLSH  BNC  FJC2 
10.10  11.10  STM  FJC1  CFTK11 
11.10  11.25  Tea/Coffee  
11.25  12.10  CFTK1  CFTK6  CFTK12 
12.20  13.05  CFTK2  CFTK7  Closing 
13.05  14.35  LUNCH  
14.35  15.00  CFTK3  CFTK8   
15.00  15.25  CFTK4  CFTK9   
15.35  16.00  CFTK5  CFTK10   
16.00  16.15  Tea/Coffee    
16.15  17.30  TUPS  TUPS   
17.30  Snacks  Snacks   
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, SpringerVerlag, 1972.
 DAVIS, J.F. and KIRK, P., Lectures Notes in Algebraic Topology, Department of Mathematics, Indiana University, Bloomington, IN 47405, Email 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, SpringerVerlag, 1997.
 HUSEMULLER Dale, Fibre bundles, GTM20, Springer, 1994.
 KERVAIRE M. and MILNOR J., *Groups of homotopy spheresI*, Annals of Mathematics, Vol. 77 (1963), 504537.
 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. 190199.
 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 19561960 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. 3955, 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 hcobordism 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), 358426.
 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 Ltheory 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, SpringerVerlag, 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.
Sr  SID  Fullname  Gender  Affiliation  State  Position in College/Univ.  Univ./ institute M.Sc./ M.A.  Year of Passing M.Sc./ M.A 
Ph.D. Degree Date 
1  3640  Dr. Somnath Basu  Male  Binghamton University  U.S.A  Visiting Assistant Professor  Indian statistical institute  2005  15 Aug 2011 
2  2874  Mr. Surojit Ghosh  Male  Ramakrisna Mission Vivekananda University  Phd student  IIT Kanpur  2012  
3  2912  Mr. Ramen Ghosh  Male  CMI, Chennai  Tamil nadu  Pass out Msc student  CMI, Chennai  2011  
4  2967  Dr. Abhijit Pal  Male  CMI, Chennai  Tamil nadu  Visiting fellow  M.Sc  2004  24 Mar 2011 
5  3271  Mr. Sanjay Kumar Singh  Male  TIFR, Mumbai  Maharashtra  Research scholar  University of Allahabad  2005  
6  3514  Mr Arghya Mondal  Male  The Institute Of Mathematical Sciences  Tamil nadu  Phd student  The Institute Of Mathematical Sciences  2012  
7  3545  Mr. Punya Plaban Satpathy  Male  IISER, Pune  Maharashtra  4th year student  Awaiting Result  
8  3565  Mr. Apurv Nakade  Male  CMI, Chennai  Tamil nadu  Ph.d  CMI, Chennai  2012  
9  3587  Mr. Devendra Tiwari  Male  TIFR, Mumbai  Maharashtra  Ph.d  BHU, Varanasi  2010  
10  3616  Mr. Karthik Chandrasekhar  Male  CMI, Chennai  Tamil nadu  Ph.d  Chennai mathematical institute  2011  
11  3628  Mr Vidyasagar Mysoremath  Male  Rani Chennamma University  Karnataka  Asst. professor  Karnatak University/M.Sc  2008  
12  3525  Mr. Sudipta Kolay  Male  CMI, Chennai  Tamil Nadu  Integrated phd  CMI, Chennai  Awaiting Result  
13  3507  Mr. Anand Bhushan Deshpande  Male  Fergusson College, Pune  Maharashtra  Research student  University of Pune  2011  
14  3249  Mr Dipendu Maity  Male  IIT, Patna  Bihar  Research scholar (phd)  Indian institute of technology kanpur  2007  
15  3522  Mr. Pradip Kumar  Male  HRI, Allahabad  Uttar Pradesh  Phd student  IIT, Kanpur  2009  
16  3117  Dr. Priyavrat Deshpande  Male  CMI, Chennai  Tamil Nadu  Postdoctoral fellow  The University Of Western Ontario  2007  31 May 2011 
17  3341  Mr. Anurag Singh  Male  IIT Kanpur  Uttar Pradesh  Student  IITGuwahati  2012  
18  3353  Mr. Kushal Lalwani  Male  Department. of Mathematics Delhi  New Delhi  M.Phil  D.U. M.A.  2011  
19  3250  Mr. Anand Kumar Tiwari  Male  IIT Patna  Bihar  Ph.D.  B.H.U  2007  
20  3104  Dr. Kamlesh Kumar Rai  Male  D.N.G.College, Itanagar, A.P.  Arunachal Pradesh  Sr Lecturer  Purvanchal / U.P.College Varanasi, UP  1995  29 Dec 2005 