5,525 reputation
1320
bio website bangor.ac.uk/r.brown
location University of Wales-Bangor, United Kingdom
age 79
visits member for 2 years, 3 months
seen 12 hours ago

I am Professor Emeritus at Bangor University. I was an undergraduate and postgraduate at Oxford University (1953-1959), where my supervisor was the inimitable Henry Whitehead. When he died suddenly in 1960, Michael Barratt took charge, and I got my DPhil in 1962. I was lecturer at Liverpool (1959-64), Senior Lecturer and then Reader at Hull University (1964-1970), and then Professor at Bangor from 1970.

I published a text "Elements of Modern Topology" with McGraw Hill in 1968, and the 3rd edition is now available as "Topology and Groupoids" from amazon, see my web page. It was writing this book, and trying to clarify certain points, such as the fundamental group of the circle, that got me into the area of groupoids; this suggested the area of higher groupoids; research on this got going in the 1970s, and has been a major area in my work, with fortunate collaborations, and contributions from research students.

You can see most of my publications on my web site, on such topics as general topology, algebraic topology, group theory, category theory, with many on aspects of groupoids and their generalisations. There are also papers on popularisation and teaching, and on the sculptor John Robinson. One main book is the editions (1968, 1988) of the book which is now "Topology and groupoids" (2006), the last published privately to keep the price down.

I am also a joint author of a 703 page book "Nonabelian algebraic topology" published in 2011 by the European Mathematical Society. It sets out a quite new framework for basic algebraic topology, based on work over 40 years, mainly jointly with Philip Higgins, on the development and applications of higher order Seifert-van Kampen theorems, and related results. A pdf is available on my web page.

I have given a number of general lectures, to audiences from children to other scientists, including a Royal Institution Friday Evening Discourse "Out of Line" in 1992. Links to this and to various articles and presentations are available from my Preprint page and from my Popularisation and Teaching page.

See also the Popularisation of Mathematics web site http://www.popmath.org.uk for symbolic sculptures and knots!


Jul
26
comment A doubt in Hatcher's Algebraic Topology.
They use paths of length $r \geqslant 0$. Then composition of paths gives a category, a concept which is useful anyway. Of course reparametrization has to be introduced at some stage. I think it makes the first steps easier.
Jul
26
comment A doubt in Hatcher's Algebraic Topology.
I am not sure why texts use only paths or length 1 instead of following the book by Crowell and Fox "Introduction to knot theory"
Jul
19
comment Describing the Wreath product categorically.
@Qiaochu Yuan: As I want to do explicit calculations, I am mainly in favour of strict structures. As an example, Chapter 11 of "Topology and Groupoids" deals with group actions and orbit spaces and gives a specific theorem on $\pi_!(X/G)$ in terms of (strict) orbit groupoids. An example computed is the symmetric square of a space. How is this related to the homotopy quotient?
Jul
17
comment Long exact sequence of a fibration, center
@user161954: Actually what you ask is not quite so direct, and is verified further on in that section using the notion of cat$^1$-group. Crossed modules are equivalent to cat$^1$-groups, and also to (edge symmetric) double groupoids with connections and one vertex, see Chapter 6. It is useful to understand all of these to see clear proofs. The "narrowest" concept, that of crossed module, is often not the easiest in which to write down proofs.
Jul
16
comment Long exact sequence of a fibration, center
Wrt my last comment, I should say "is not set up at the space level" rather than "does not work".
Jul
16
comment Long exact sequence of a fibration, center
@user161954: I do not have an immediate answer to your question which is a good one, partly as I see this area more from the double groupoid viewpoint, which is pursued in Chapter 6 of the book. You might also like to look at [129] on my publication list, but that does not work at the space level. I'll think on it.
Jul
16
revised Are these two spaces homotopy equivalent?
added a bit more explanation
Jul
16
revised Are these two spaces homotopy equivalent?
corrected second picture and explained it isd only pair of points identified
Jul
14
revised Long exact sequence of a fibration, center
typo
Jul
14
answered Long exact sequence of a fibration, center
Jul
11
answered Expressing homotopy groups of spaces of (unpointed) maps $S^1\to M$ in terms of homotopy groups of spaces of pointed maps.
Jul
8
revised Explicit expression for homeomorphism and homotopy equivalence
added a comment on Grothendieck.
Jun
30
answered How to study math to really understand it and have a healthy lifestyle with free time?
Jun
30
revised Singular $\simeq$ Cellular homology?
added detail of the proposition
Jun
29
answered Singular $\simeq$ Cellular homology?
Jun
26
answered Cardinality of fibers of covering map and the fundamental group of E
Jun
23
revised Explicit expression for homeomorphism and homotopy equivalence
added a mathoverflow link
Jun
21
revised fibre of a fibration is homotopy equivalent to its homotopy fibre
correct reference numbers
Jun
21
revised Do homotopy pullbacks preserve weak homotopy equivalences?
correct reference
Jun
21
revised fibre of a fibration is homotopy equivalent to its homotopy fibre
typo