ISL Geometric Topology (2014)

Venue: BHU, Varanasi
Dates: 7th –  19th July, 2014


Convener(s) Speakers, Syllabus and Time table Applicants/Participants


School Convener(s)

Name C.S. Aravinda B. Tiwari Mukut Mani Tripathi
Mailing Address Associate Professor,
Department of Mathematics,
TIFR CAM, Sharadanagar, GKVK Post, Bangalore-560065.
Associate Professor,
DST-CIMS, Faculty of Science,
BHU Varanasi-221005
Department of Mathematics,
BHU Varanasi-221005


Speakers and Syllabus 

 Overview: Basic focus in this workshop is a discussion of the topology of curves, surfaces, and to give an introduction to Algebraic Topology through a discussion of homotopy, fundamental group and covering spaces. Main emphasis will be to explain concepts through examples. Below is a more descriptive information about the syllabus.


Theme 1: Definition of manifolds as submanifolds of Rn , and tie this up with the standard abstract definition by discussing a proof of ‘medium form’ of the Whitney embedding theorem for compact manifolds.

Theme 2: Proof of triangulation of closed surfaces, classification theorem for surfaces. Discuss orientability, and show that closed surfaces embedded m in R3 are necessarily orientable.

Theme 3: A discussion of quotient topology, group actions, quotient spaces, projective plane and Klein bottle. Embeddings of projective plane and Klein bottle in R4 .

Theme 4: A discussion of homotopy, path homotopy, homotopy equivalence, fundamental groups, covering spaces. Discuss fundamental groups of sphere, projective plane, torus, Klein bottle etc. and a covering space proof of Jordan curve theorem.


Date 9:00-10:00 10:30-11:30 11:45-12:45 15:00-16:00 16:30-17:30
7/07/2014 L1(AKS) L2(MMT) L3(MS) T1 T2
8/07/2014 L4(MMT) L5(MS) L6(AM) T3 T4
9/07/2014 L7(MS) L8(AM) L9(KV) T5 T6
10/07/2014 L10(MS) L11(AM) L12(KV) T7 T8
11/07/2014 L13(KV) L14(HP) L15(AM) T9 T10
12/07/2014 L16(KV) L17(SP) L18(CSA) - -
14/07/2014 L19(CSA) L20(SP) L21(VA) T11 T12
15/07/2014 L22(MKV) L23(SP) L24(VA) T13 T14
16/07/2014 L25(MKV) L26(SP) L27(VA) T15 T16
17/07/2014 L28(MKV) L29(SP) L30(VA) T17 T18
18/07/2014 L31(MKV) L32(VA) L33(GS) T19 T20
19/07/2014 L34(GS) L35(VA) L36(GS) - -
  • Ln indicates Lecture no. n
  • Tn indicates Tutorial no. n
  • Tea Breaks: 10:00 - 10:30 and 16:00 - 16:30
  • Lunch Break: 12:45 - 15:00

Speakers and Topics

Speakers Topics
A K Srivastava (AKS) Urysohn lemma and Metrization.
M M Tripathi (MMT) Brief review of multivariable calculus, bump functions, partition of unity.
Mahender Singh (MS) Quotient topology, Group actions, quotient spaces,Projective plane, Klein bottle.
Anandateertha Mangasuli (AM) Definition of smooth manifolds as sub-manifolds of Rn , abstract definition by smoothness of transition functions,‘medium form’ of the Whitney embedding theorem for compact manifolds.
Keerti Vardhan Madahar (KV) Proof of triangulation of closed surfaces, and Classification theorem for surfaces.
Harish Chandra Pathak (HP) Sard’s theorem.
Suhas Pandit (SP)  Homotopy, path homotopy, homotopy equivalence,
Fundamental groups, covering spaces.
C S Aravinda (CSA) Orientation and Gauss-Bonnet theorem.
Vikram Aithal (VA) Embeddings of Projective plane and Klein bottle in R4 , Lens spaces; covering space proof of Jordan curve theorem.
M K Vemuri (MKV) Transversality, orientability of closed surfaces in R3 .
G Santhanam (GS) Discuss fundamental groups of sphere, projective
plane, Torus, Klein bottle.

Reference Books: The following books are the suggested references:

  1.  A first course in Topology By Munkres.
  2.  Elementary Differential Geometry By Christian Ba ̈r.
  3.  Differential Topology By V. Guillemin and G. Pollack.


Selected Applicants


  • Participants are advised to confirm their participation by sending their to and fro tickets latest by 30th May.
  • Please note no travel support will be provided by the host institution to any participant of the ISL.
Sr. SID Full Name Gender Affiliation City and State Position University/  Institute M.Sc./M.A. Year of Passing M.Sc./ M.A Ph.D. Degree Date
1 5350 Ms Priyambada Tripathi Female Shaheed Bhagat Singh College, University Of Delhi South Delhi, Delhi Asst. Prof. BHU 2008  
2 5362 Dr Anugraha Nidhi Mohapatra Male Goa University Panaji, Goa Asso. Prof. Sambalpur University 1985 26 Feb 1992
3 5421 Dr Shamsur Rahman Rahman Male Maulana Azad National Urdu University Hyderabad , Andhra Pradesh   V.B.S. Purvanchal University Jaunpur 2004 15 Dec 2006
4 5434 Dr Bipul Sarma Male MC College Barpeta, Assam Asst. Prof. Gauhati University 1999 19 Aug 2006
5 5482 Mr. Kulajit Pathak Male B. H. College Howly, Assam Asst. Prof. Gauhati University 1996  
6 5527 Dr. Punam Gupta Female Dr. Hari Singh Gour University Sagar, Madhya Pradesh Asst. Prof. BHU 2007  
7 5604 Dr. Manoj Kumar Singh Male UIET,CSJM University Kanpur Kanpur, Uttar Pradesh Asst. Prof. Ddu Gorakhpur University 2006 16 Feb 2010
8 5643 Dr. Gauree Shanker Male Banasthali University Tonk, Rajasthan Asso. Prof. Ddu Gorakhpur University 2000 8 Oct 2005
9 5644 Mr. Abhishek Mukherjee Male Kalna College Burdwan, West Bengal Asst. Prof. The University Of Burdwan 2007  
10 5667 Mr Vishal Gupta Male Zakir Husain Delhi College (University Of Delhi) Delhi Asst. Prof. IIT Guwahati 2010  
11 5673 Dr. Brijesh Kumar Tripathi Male Central Institute Of Plastics Engineering And Technology Lucknow Lucknow, U.P Lecturer Ddu Gorakhpur University 2002 8 Mar 2006
12 5705 Dr. Narinder Sharma Male G.G.M Science College Jammu J&K Asst. Prof. 2004 2004 31 Oct 2012
13 5736 Dr. Vinit Kumar Chaubey Male Ansal Technical Campus, Lucknow Lucknow, U.P Asst. Prof. DDU Gorakhpur University, Gorakhpur 2005 19 Jun 2009
14 5761 Dr Janardan Singh Male Gandhi College Jhunsi, Allahabad, U.P Lecturer University of Allahabad 2001 12 Jul 2006
15 5764 Dr. Shyam Kishor Male University Of Lucknow Lucknow, U.P Asst. Prof. Allahabad University 2005 11 May 2011
16 5779 Dr. Shiv Sharma Shukla Male University of Allahabad Allahabad, UP Asst. Prof. University of Lucknow 1993 10 Jun 2001
17 5966 Dr Avijit Sarkar Male University of Kalayni Kalyani, West Bengal Asst. Prof. University of Kalayni 2002 2 Feb 2010
18 5978 Dr Atasi Deb Ray Female West Bengal State University, Barasat Kolkata, West Bengal Asst. Prof. University of Calcutta 1994 5 May 2000
19 6028 Mr. Nirabhra Basu Male Bhawanipur Education Society College Kolkata, West Bengal Asst. Prof. Hyderabad University 2009  
20 6056 Mr. Kalyan Halder Male Sidho-Kanho-Birsha University Purulia, West Bengal Asst. Prof. Jadavpur University 2009  
21 6067 Mr. Dattatray Renukadas Patil Male B. N. S. Science College, Sangamner Sangamner, Maharashtra Asst. Prof. University of Pune 2004  
22 6069 Ms. Srimayee Samui Female Umeschandra College Kolkata, West Bengal Contractual Lecturer Jadavpur University 2010  
23 6085 Dr. Vibha Srivastava Female Sri Jai Narain P.G. College(K.K.C) Lucknow, U.P Lecturer Lucknow University 2009 9 Jan 2014
24 6126 Mr. Yashpaul Male Malwa College Bondli Samrala Samrala District Ludhiana, Punjab Asst. Prof. Government College Hoshiarpur Punjab 2005  
25 6193 Dr. Satya Prakash Yadav Male SIET, Allahabad Allahabad, Uttar Pradesh Asst. Prof. University of Allahabad 2004 15 Oct 2010
26 6210 Ms. Jita Parida Female Priyadarshini Indira Mahavidyalaya, Junagarh, Odisha. Junagarh, Orissa Lecturer Sambalpur University 2004  
27 6211 Dr. Subramania Pillai I Male Pondicherry University, Puducherry-605014 Kalapet, Pondicherry Asst. Prof. University of Hyderabad 2003 15 Mar 2010
28 6229 Dr. Shravan Kumar Pandey Male A.P.S.University, Rewa (M.P.) Rewa, Madhya Pradesh Guest Lecturer A.P.S.University, Rewa (M.P.) 2007 3 Aug 2013
29 6230 Dr. Giteshwari Pandey Female A.P.S.University, Rewa (M.P.) Rewa, Madhya Pradesh Guest Lecturer A.P.S.University, Rewa (M.P.) 2007 5 Aug 2013
30 6250 Dr. Dipankar Debnath Male Bamanpukur High School Nabadwip, West Bengal Asst. Prof. University Of Kalyani 2004 8 Sep 2010
Local Participants
31 5774 Dr. Manish Kumar Gupta Male U.P.College,Varanasi Varanasi, U.P Associate Professor D.D.U. Gorakhpur University 2002 17 Apr 2006
32 5479 Dr Mrs Sangita Srivastava Female H.C.P.G.College Varanasi, U.P Associate Professor University of Allahabad, Allahabad 1987 22 Feb 1993
33 5351 Mr. Manoj Kumar Male Dst-Cims, Banaras Hindu University Varanasi, U.P PhD Dr. R. M. L. Awadh University Faizabad 2008  
34 5399 Mr. Anjani Kumar Shukla Male DST-CIMS, FACULTY OF SCIENCE, BANARAS HINDU UNIVERSITY Varanasi, U.P PhD Dr. R. M. L. Awadh University Faizabad 2008  
35 5354 Mr Ghanashyam Kumar Prajapati Male BHU Varanasi, U.P PhD U.P.College,Varanasi 2009  
36 5359 Mr. Dinesh Kumar Male BHU Varanasi, U.P Ph.D. Allahabad University 2008  
37 5571 Mr. Ranadip Gangopadhyay Male BHU Varanasi, U.P PhD Student Netaji Subhas Open University 2013  
38 5675 Ms. Seema Mishra Female Indian Institute of Technology(B.H.U.) Varanasi, U.P PhD student University of Allahabad 2012  
39 5749 Ms. Vandana Tiwari Female IIT(BHU), Varanasi Varanasi, U.P PhD IIT KANPUR 2010  
40 5688 Ms. Reshma Singh Female IIT BHU Varanasi, U.P PhD University of Allahabad 2011  
41 5794 Mr. Sandeep Kumar Porwal Male BHU Varanasi, U.P PHD BHU 2007  
42 5627 Mr Deepak Rout Male BHU Varanasi, U.P PHD Utkal University 2007  
43 5772 Mr Shiva Sharma Male IIT-BHU Varanasi, U.P PhD BHU, Varanasi 2012  
44 5907 Mr.Prashant Kumar Mishra Male IIT(BHU) Varanasi, U.P Ph.D Student Banaras Hindu University 2011  
45 5911 Mr. Vijay Kumar Yadav Male IIT(BHU) Varanasi, U.P Ph.d(Pur.) Dr. RMLAU Faizabad Uttar Pradesh 2012  
46 6196 Mr. Sheo Kumar Singh Male BHU Varanasi, U.P Ph.D. student Banaras Hindu Univ., Varanasi 2006  
47 6246 Mr. Dheeraj Shukla Male BHU Varanasi, U.P Research Scholar( PhD) Banaras Hindu University 2010  
Waiting List
1 5760 Mr Anoop Rs Male NIT Calicut Kozhikode, Kerala Adhoc faculty CUSAT, COCHIN 2008  
2 6243 Mr. Anand Bhushan Deshpande Male Centre for Post-graduate Studies, Sir Parshurambahu College Pune, Maharashtra Visiting Faculty University of Pune 2011  
3 5942 Mrs Sushma Virendrasinh Parmar Female assms institute of information technology pune Pune, Maharashtra assistant professor north maharashtra jalgoan university 1999  
4 6235 Mr. Gobinda Chandra Panda Male M.I.E.T,B.P.U.T Bbsr, Orissa Asst. Professor Sambalpur University 2005  
5 5559 Ms. Ruchi Kaushik Female Banasthali University Jaipur, Rajasthan Reseach Associate M.Sc. 2010  
6 6026 Ms Anu Devgan Female Punjabi University, Patiala. Patiala, Punjab PhD Panjab University, Chandigarh 2010  
7 6024 Ms Ankita Rai Female D.D.U. Gorakhpur Gorakhpur, U.P Ph.D Research Scholar D.D.U. Gorakhpur 2010  
8 6218 Mr. Kushal Lalwani Male University of Delhi New Delhi, Delhi Research Scholar D.U. 2011  
9 5560 Mr. Akhilesh Yadav Male University of Allahabad, Allahabad. Allahabad, U.P Research Scholar University of Allahabad, Allahabad. 2008  
10 5656 Mr. Uma Shankar Verma Male Department of Mathematics,
University of Allahabad
Allahabad, U.P Research Scholar University of Lucknow, Lucknow 2006  
11 5450 Mr. Ganga Prasad Yadav Male University of Allahabad, Allahabad Allahabad, U.P D.Phil. Student University of Allahabad, Allahabad 2011  
12 5438 Ms. Sweta Kumari Female University of Allahabad Allahabad, U.P D. Phil. Student University of Allahabad 2009  
13 6192 Mr Vivekanand Yadav Male D.D.U. Gorakhpur Gorakhpur, U.P Ph.D. D.D.U. Gorakhpur 2008  
14 6202 Mr. Gyanvendra Pratap Singh Male D.D.U. Gorakhpur Gorakhpur, U.P Research Scholar D.D.U. Gorakhpur 2009  
15 5575 Mr. Soumya Dey Male IISER Mohali Mohali, Chandigarh PhD  Student RKM Vivekananda University 2013  
16 6247 Mr. Kamran Khan Male Aligarh Muslim University Aligarh, U.P PhD Aligarh Muslim University, Aligarh 2009  
17 6248 Mr Mohammad Shuaib Male Aligarh Muslim University Aligarh, U.P PhD Aligarh Muslim University, Aligarh 2006  
18 6090 Mr. Manik Das Male University of Calcutta Kolkata, W.B Ph.D Student Visva-Bharati 2012  
19 5830 Mr. Dhriti Sundar Patra Male Jadavpur University Kolkata, W.B PhD IIT Bombay 2011 24 Sep 2013
20 5884 Mrs. Barnali Laha Female Jadavpur University Kolkata, W.B Junior Research Fellow Jadavpur University 2010  
21 5807 Mr. Buddhadev Pal Male Jadavpur University Kolkata, W.B Post Doc. Fellow (NBHM) Jadavpur University 2009  
22 6108 Mr. Santu Dey Male Kolkata Kolkata, W.B Research Scholar Kolkata 2012  
23 5668 Ms. Sunanda Sinha Female University of Calcutta Kolkata, W.B Ph.D. Student University of Calcutta 2010  
24 5349 Mr Santanu Acharjee Male Institute of Advanced Study in Science and Technology. Gauhati, Assam Ph.D Research Scholar Gauhati University 2011  
25 5924 Dr Alety Srisailam Renikunta Male Kakatiya University Warangal, A.P postdoctoral Research Work Osmainia University 2006 20 Jun 2011
26 5641 Ms. Snigdha Bharati Choudhury Female NIT Rourkela Rourkela, Orissa Ph.D Utkal University, Bhubaneswar 2011  
27 5607 Ms. Mitali Routaray Female National Institute Of Technology Rourkela, Orissa PhD Utkal University, Vanivihar 2012  


How to reach

The venue, DST-Centre for Interdisciplinary Mathematical Sciences, of the ISL on Geometric Topology situated in the campus of  Banaras Hindu University, Varanasi (U.P); which is 8 Km far from Varanasi Cant railway station, 20Km from Mughalsarai railway station and 30 Km from the Varanasi airport.