Algebraic Topology I
Math 537
|
Algebraic Topology I Math 537 |
Instructor Prof.
Sergey Finashin
The main Textbook
Allen
Hatcher Algebraic
Topology I available
online
More textbooks:
1. Glen E. Bredon Topology and Geometry,(Springer,
1995), Chapters 3-5
2. Joseph J. Rotman An Introduction to
Algebraic Topology, (Springer, 1988), except Chapters
9, 11
3. A. T. Fomenko, D. B. Fuks A Course
in Homotopy Topology
4. O. Ya. Viro, O. A. Ivanov, N, Yu. Netsvetaev, V.M. Kharlamov
Elementary
Topology - A First Course - Textbook in Problems,
(available online, see a reference on my
web-page), chapter 4
5. Lecture Notes in Topology by Sossinski (for Moscow Independent University)
(useful reading, although a bit too elementary and not very relevant
to our course)
Introduction
("What is Topology ?", Brauer's fixed point theorem, topological constructions)
Surfaces
(PL-surfaces, the Euler characteristic)
Configuration
systems (a base of topology, mechanical systems)
Vector
fields on a plane (singular points, the index of a vector field)
Vector
fields on surfaces (Poincare index theorem, applications)
Infinite
constructions (The Cantor set, Peono's curve, Antoine's necklege, Brouer's
continuum, Alexander's horned sphere;
homotopy equivalence, degree of a map of a circle to itself)
Curves
on a plane (immersed curves and regular homotopies, Whitney index,
the fundamental theorem of algebra)
1. Homotopy and Homotopy Type, Cell Complexes (Chapter 0)
2. Fundamental Groups (1.1 - 1.2)
3. Covering Spaces (1.3)
Midterm I
November 11, 11:00
4. Simplicial and Singular Homology Groups (2.1)
5. Computation of Homology Groups (2.1 - 2.2)
6. Some Applications of Homology (2.2)
Midterm II
December 23
7. The formal Viewpoint (2.3)
8. Cohomology Groups (3.1 and partially 3.2 - 3.3)
Final
Homework II Fundamental Group and Covering Spaces dvi-file ps-file (zipped)
Homework III (problems from Hatcher's textbook)
Problems of Midterm II: dvi ps ps-zipped