Text similar to chapter 9 of Topology from James Munkres

Question

I'm self-studying chapter 9 of Topology from James Munkres.

I like to read different books about the same topic at the same time. Can someone recommend some text/book that is about the same subjects as found in chapter 9?

This chapter is about the fundamental group. It is from part 2 of the book, which is called algebraic topology. The sections are called homotopy of paths, the fundamental group, covering spaces, the fundamental group of the circle, retractions and fixed points, the fundamental theorem of algebra, the Borsuk-Ulam theorem, deformation retracts and homotopy type, the fundamental group of S* and fundamental groups of some surfaces.

Thanks in advance !

Answer 1

Algebraic Topology by F.H Croom will be a good choice for a beginner in algebraic topology

Answer 2

John M.Lee's Introduction to Topological Manifolds is in many ways a more modern, more geometrically themed version of Munkres. I consider it the prototype for a comprehensive first course in topology at the upper level undergraduate/first year graduate level.I also think it will serve a student a lot better then Munkres in preparing them for a serious graduate course in algebraic topology while still teaching them all the basics, including the elements of category theory and diagram chasing. There are lots of terrific books on topology,but I think that one is probably closest to what you're looking for.

Answer 3

Massey's "A Basic Course in Algebraic Topology" or Hatcher's "Algebraic Topology".

Answer 4

My book Topology and Groupoids is the only text that fully treats these topics in $1$-dimensional homotopy theory from the modern viewpoint of groupoids. It includes results on orbit spaces not available elsewhere, and a useful gluing theorem for homotopy equivalences.

I also mention that this book is one of the few that defines a path of length $r \geqslant 0$ in a space $X$ to be a map $a: [0,r] \to X$. If paths of length $r,s$ are composable then their composite is of length $r+s$, which makes sense intuitively, and the composition is then associative and with strict identities. This saves a certain amount of bother. One defines paths $a,b$ to be equivalent if there are constant paths $u,v$ such that $u+a,v+b$ are defined, are of the same length, and are homotopic rel end points in the usual sense. This gives a definition of the fundamental groupoid $\pi_1 X$.

The book does not include the fundamental groups of surfaces, which is well treated in several books, and also in the book "Knots and surfaces" by Gilbert and Porter, (OUP) (1996).

Answer 5

Here is a cocktail of sources that are quite helpful

1) Chapter III from Gamelin and Greene "Intro to Topology."

http://www.amazon.com/Introduction-Topology-Second-Edition-Mathematics/dp/0486406806

2) An excellent chapter by John Lee on Simply Connected Spaces

http://www.math.washington.edu/~lee/Courses/441-2012/simplyconn.pdf?v2

3) An extremely nice set of videos by NJ Wildberger - several of which clearly present homotopy, the fundamental group, and covering spaces. There are plenty of examples and lots of pictures which add an intuitive understanding to the rigor:

https://www.youtube.com/playlist?list=PL41FDABC6AA085E78