Spring 2017
Course Information
| Course | MATH 7321 · Topology 3 |
| Instructor | Alex Suciu |
| Course Web Site | https://suciu.sites.northeastern.edu/courses/math7321-spring2017/ |
| Time and Place | Tuesday & Thursday 4:10–5:40pm in 544 NI |
| Office | 435 LA – Lake Hall |
| a.suciu@northeastern.edu | |
| Office Hours | Tuesday & Thursday 3:00–4:00pm in 435 LA |
| Prerequisites: | MATH 7221 – Topology 2 |
Course Description
| This is a course in classical Algebraic Topology, and some of its applications. Topics we may cover include: Higher homotopy groups, cofibrations, fibrations, fiber bundles, homotopy sequences, homotopy groups of Lie groups and associated manifolds, cellular approximation, Hurewicz theorem, Whitehead theorem, Eilenberg-MacLane spaces, obstruction theory, Postnikov towers, H-spaces and Hopf algebras, Bockstein homomorphism, Poincaré-Lefschetz duality, Alexander duality, Euler class, Gysin sequence, cobordism, intersection form, signature, plumbing, cohomology of fiber bundles, classifying spaces, characteristic classes, spectral sequences, Steenrod squares. We will cover material selected from the following textbooks: |
- Algebraic Topology, by Allen Hatcher, Cambridge University Press, 2002. MR.
- Topology and Geometry, by Glen Bredon, GTM No. 139, Springer-Verlag, 1997. MR.
- Modern classical homotopy theory, by Jeffrey Strom, Graduate Studies in Mathematics, vol. 127, American Mathematical Society, Providence, RI, 2011. MR.
- Lecture Notes in Algebraic Topology, by James F. Davis and Paul Kirk, Graduate Studies in Mathematics, vol. 35, American Mathematical Society, Providence, RI, 2001. MR.
| Here are some other useful references, and material for further reading: |
- Elements of Homotopy Theory, by George W. Whitehead, GTM No. 61, Springer-Verlag, 1979. MR.
- Algebraic Topology, by Edwin H. Spanier, Corrected reprint, Springer-Verlag, 1981. MR.
- Cohomology operations and applications in homotopy theory, by Robert Mosher and Martin Tangora, Harper and Row, New York-London, 1968. MR.
- A user’s guide to spectral sequences, by John McCleary, second edition, Cambridge Studies in Advanced Math, no. 58, Cambridge University Press, 2001. MR.
- Characteristic Classes, by John W. Milnor and James Stasheff, Ann. Math. Studies, No. 76, Princeton University Press, 1973. MR.
- The topology of fibre bundles, by Norman Steenrod, reprint of 1951 edition, Princeton University Press, 1999. MR.
- Spectral Sequences in Algebraic Topology, by Allen Hatcher, draft book, 2004.
- A Concise Course in Algebraic Topology, by J. Peter May, Chicago Lectures in Mathematics, University of Chicago Press, Chicago, IL, 1999. MR.
Homework assignments
- Homework 1: Hatcher, Chapter 3.3, pp. 257-259: Problems 2, 3&4, 5, 6, 10, 24. Due January 19.
- Homework 2: Hatcher, Chapter 3.3, pp. 258-260: Problems 7&9, 25, 26, 28, 29, 32&33. Due February 2.
- Homework 3: Due February 16.
- Homework 4: Hatcher, Chapter 4.1, p. 358, Problem 17; Chapter 4.2, p. 392, Problem 34; Chapter 4.G, p. 460, Problem 1; Chapter 4.H, p. 466, Problems 1, 2; Chapter 4.I, p. 469, Problem 1. Due March 2.
- Homework 5: Due April 4.
- Homework 6: Due April 25.