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16h
revised Eckmann-Hilton and higher homotopy groups
typo
Feb
9
answered Fundamental group and path-connected
Feb
9
revised Non-abelian fundamental group on a path-connected space
added an explanatory comment
Feb
8
answered to understand a theorem for fundamental group
Feb
8
revised Non-abelian fundamental group on a path-connected space
added a bit more
Feb
8
answered Non-abelian fundamental group on a path-connected space
Jan
25
comment Tensor product of monoids and arbitrary algebraic structures
Considering the dates and number of authors on my bibliography of the nonabelian tensor product, don't call it "your work". I am of course pleased to have a hand in it.
Jan
23
revised Universal cover via paths vs. ad hoc constructions
extra info on the construction of covering spaces
Jan
22
comment Complement of the Solid Torus in $S^3$ is Again a Solid Torus
see also math.stackexchange.com/questions/195848/…
Jan
22
comment Complement of the Solid Torus in $S^3$ is Again a Solid Torus
I tried to find a movie of this, but I did find dimensions-math.org/Dim_CH7_E.htm on the Hopf map which could help your imagination. Try drawing a picture of the $xz$-plane, cutting the solid torus in 2 disks. The $z$-axis is a vertical line. Then on each side of this we have a family of circles round the two disks, getting larger and larger, and "nearer" to the $z$-axis.. This picture then rotates about the $z$-axis.
Jan
21
revised Complement of the Solid Torus in $S^3$ is Again a Solid Torus
typo
Jan
21
answered Complement of the Solid Torus in $S^3$ is Again a Solid Torus
Jan
21
comment On the surjectivity of the Hurewicz homomorphism
Just for a bit of extra precision on the ticked answer, I suggest replace $1 \leq i \leq k$ by $0 \leq i \leq k$, especially as homotopy groups are defined only for spaces with base point.
Jan
19
revised how to calculate relative homotopy groups?
extra info
Jan
19
comment how to calculate relative homotopy groups?
@Najib Idrissi Just to point out that the work mentioned in my answer shows there are non ad hoc ways of dealing with relative homotopy groups. For more background, see presentations on my preprint page pages.bangor.,ac.uk/~mas010/brownpr.html, e.g. Aveiro, Galway.
Jan
18
answered how to calculate relative homotopy groups?
Jan
15
comment Long Exact sequence of Relative Homotopy Groups: examples and applications
@Mike Miller: I'll see what I can cook up; we wrote 35. (R. Brown and J. HUEBSCHMANN), ``Identities among relations'', in Low dimensional topology, London Math. Soc. Lecture Note Series 48 (ed. R. Brown and T.L. Thickstun, Cambridge University Press, 1982), pp. 153-202.a long time ago! Some of this is in Section 3.1 of the above book.
Jan
15
answered Long Exact sequence of Relative Homotopy Groups: examples and applications
Jan
15
comment basic intuition of fundamental groups
I have felt for 50 years or so that the more intuitive and more powerful approach is via the fundamental groupoid on a set of base points, and this may be found in English only in my book "Topology and Groupoids" pages.bangor.ac.uk/~mas010/topgpds.html, first (differently titled) edition 1968. For example, the basic Seifert-van Kampen theorem then allows the computation of the fundamental group of the circle, and much more. Also I allow paths as maps $[0,r] \to X$ for $r \geqslant 0$, which saves bother.
Jan
11
revised $S^m * S^n \approx S^{m+n+1}$
typo: 1 should have been r_1