# Introduction to Algebraic Topology (Part-II)

By Prof. Anant R. Shastri   |   IIT Bombay
Learners enrolled: 440
As stated above, this is PG level course in Mathematics, which requires basic knowledge of Linear algebra, Point set topology, and group theory. This course is central to many areas in modern mathematics. The subject itself saw tremendous growth during 1950 and currently has attained a matured status.
The syllabus I have chosen is common to MA5102 at IIT Bombay and AFS-III program of National Centre for Mathematics. It has enough material common to the syllabus followed by several Universities and IIT’s in the country and goes beyond. Nevertheless it has different flavour liked by variety of students. I have published a book in which one-third of the content is roughly the present course. This book is followed by several universities abroad also for their course.

INTENDED AUDIENCE : Anybody who would like to get trained in Algebraic Topology such as Computer scientists, Electrical , Aerospace engineers and mathematicians, and physicists.

PREREQUISITES     : Point Set Topology is pre-requisite. Exposure to Basics of Linear algebra and Group theory is preferred. Preferably attended Algebraic Topology Part-I course offered by the same instructor

INDUSTRIES  SUPPORT  : All IIT’s, IISERs , TIFR and Universities in India.

Summary
 Course Status : Completed Course Type : Elective Duration : 12 weeks Category : Mathematics Credit Points : 3 Level : Undergraduate/Postgraduate Start Date : 26 Jul 2021 End Date : 15 Oct 2021 Enrollment Ends : 09 Aug 2021 Exam Date : 23 Oct 2021 IST

Note: This exam date is subjected to change based on seat availability. You can check final exam date on your hall ticket.

### Course layout

Week-1:What is Algebraic Topology: Notion of Homotopy.
Week-2:Categories and Functors
Week-3:Basic Homological Algebra
Week-4:Singular Homology
Week-5:Computations with simple objects
Week-6:Review of Simplicial complexes and Simplicial homoloy
Week-7:Euler Characteristic, Lefschetz Number
Week-8:Relation between fundamental groups and 1st homology
Week-9:Applications homology: Brouwer’s invariance of domain
Week-10:Applications continued. Lefschetz Fixed point theorem
Week-11:CW complexes and CW homology
Week-12:Discussion for future topics.

### Books and references

1. Anant R. Shastri Basic Algebraic Topology, CRC Press, 2014
2. M.J. Greenberg and J. R. Harper, Algebraic Topology, A first course, Benjamin/Cummings Pub. Co. 1981.
3. J. R. Munkres, Topology Iied Printice Hall.
4. Plan to provide full text of the lecture notes (link should be provided)

### Prof. Anant R. Shastri

IIT Bombay
I am a retired Emeritus Fellow of Department of Mathematics I.I. T. Bombay. After serving in School of Mathematics T.I.F.R. for 16 years I joined I.I.T. Bombay as a full professor in 1988.Apart from several research papers,in Algebraic and Differential Topology, Algebraic Geometry, Relativity theory, Group theory, etc.,I have published three books.Since 2004, I have constantly involved in the activities of ATM schools, The chief activity of these schools is to impart advanced training in Mathematics to Ph. D. students in various universities and research institutions in the country. These activities were initially funded by NBHM and currently adapted by National Centre for Mathematics, I.I.T. Bombay.Over the years, I have taught, roughly the contents of the proposed course more that 20 times to M.Sc/ BTech / MTech and Ph. D. students.CDEEP has recorded my lectures on Complex Analysis MA205 for B. Tech students, in 2008.

### Course certificate

The course is free to enroll and learn from. But if you want a certificate, you have to register and write the proctored exam conducted by us in person at any of the designated exam centres.
The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).
Date and Time of Exams: 23 October 2021 Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm.
Registration url: Announcements will be made when the registration form is open for registrations.
The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published. If there are any changes, it will be mentioned then.
Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc.

CRITERIA TO GET A CERTIFICATE

Average assignment score = 25% of average of best 8 assignments out of the total 12 assignments given in the course.
Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75. If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.

Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIT Bombay.It will be e-verifiable at nptel.ac.in/noc.

Only the e-certificate will be made available. Hard copies will not be dispatched.

Once again, thanks for your interest in our online courses and certification. Happy learning.

- NPTEL team