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May
17
comment How to compute the fundamental group of $S^2 / A$, where $A$ is a finite set of points?
You might have a look at arXiv:1404.0556 for a recent use of groupoids. There are not many texts which mention free groupoids on (directed) graphs, an obvious enough idea in this day and age. Good luck!
May
17
revised Best book for topology?
corrected a link and added one
May
16
revised How to compute the fundamental group of $S^2 / A$, where $A$ is a finite set of points?
added a link to mathoverflow
May
16
revised How to compute the fundamental group of $S^2 / A$, where $A$ is a finite set of points?
clarified a reference
May
16
answered How to compute the fundamental group of $S^2 / A$, where $A$ is a finite set of points?
May
14
answered Product of CW complexes question
May
11
answered Homotopy equivalence between $X/A$ and $X$?
May
11
revised Homotopy equivalence of certain kinds of adjunction spaces
added a lnk
May
11
revised Mayer-Vietoris Type Sequence For Pushouts
typo
May
5
comment Reviewing the basics of algebraic topology for further deeper study
Relevant to this discussion is the use of groupoids as more poowerful than groups in algebraic topology. See the discussion at mathoverflow.net/questions/40945/…
May
4
comment Text similar to chapter 9 of Topology from James Munkres
I wonder why so many algebraic topology books ignore the arguments for groupoids and more than one base point as presented for example in mathoverflow.net/questions/40945/…. I also find the arguments for some treatment of knots compelling, since the examples are so clear to students, and also to children and non mathematicians. See the web page www.popmath.org.uk for some knot sculptures and a knot exhibition.
May
3
comment Reviewing the basics of algebraic topology for further deeper study
See also the discussion on math.stackexchange.com/questions/778483/…
May
2
revised Text similar to chapter 9 of Topology from James Munkres
explains paths of various lengthss
May
2
answered Text similar to chapter 9 of Topology from James Munkres
Apr
30
comment Does the pullback of a covering space correspond to the pullback of the corresponding representation of $\pi_1$?
You can avoid the base points if you use the description of covering maps of spaces in terms of covering morphisms of groupoids, as described in my book "Topology and Groupoids". This applies in particular to pullbacks.
Apr
28
comment Necessary and sufficient condition for existence of a deck transformation
Since algebraic topology is about modelling topology by algebra, it should be pointed out that the theory of covering spaces is well modelled by the theory of covering morphisms of groupoids. See expositions of the latter in Higggins' book "Categories and groupoids" (tac.mta.ca/tac/reprints/articles/7/tr7abs.html) and my book "Topology and groupoids" (amazon).
Apr
25
comment Suggestion about Algebraic Topology talk
Good! What I have found fun is the pentoil trick, which you will find on my talk at Liverpool, What is and what should be `Higher dimensional group theory'? Dec 2009. I have travelled many places carrying a copper tubing pentoil and trefoil, and a nice length of rope, and brought members of the audience out to help with taking the loop off the knot. The knots themselves were made by a University workshop. And of course the relations at a crossing are really an application of SvKT. See also pages.bangor.ac.uk/~mas010/outofline/motion.html#motion .
Apr
25
revised Suggestion about Algebraic Topology talk
added more information
Apr
24
revised Suggestion about Algebraic Topology talk
added the notion of "anomaly"
Apr
24
answered Suggestion about Algebraic Topology talk