6,148 reputation
11321
bio website bangor.ac.uk/r.brown
location University of Wales-Bangor, United Kingdom
age 79
visits member for 2 years, 7 months
seen 14 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!


Dec
30
answered Examples of failure of excision for homotopy groups ($\pi_k(X, A)$ is not $\pi_k(X/A, *)$)
Dec
30
revised Failure of excision for $\pi_2$
added explanation
Dec
30
revised Failure of excision for $\pi_2$
added explanation
Dec
29
answered Failure of excision for $\pi_2$
Dec
21
answered Trying to understand the fibre product in the category of spaces over $X$
Dec
18
answered In a groupoid, do any two objects have a morphism between them?
Nov
22
answered Fundamental group of the topological space obtained by identifying the four vertices of a square
Nov
16
answered Use of Low dimensional Paths vs High dimensional Cubes
Nov
9
revised HNN extensions as fundamental groups
typo
Nov
9
revised HNN extensions as fundamental groups
more detail added
Nov
8
answered HNN extensions as fundamental groups
Nov
6
answered How To Present Algebraic Topology To Non-Mathematicians?
Nov
5
comment A question about the proof of the fact that contractible spaces are simply connected
To add to the previous comment, for me the potential of groupoids opened out new worlds. The clear question was: if groupoids are useful in 1-dimensional homotopy theory, can they be useful in higher dimensional homotopy theory? Or not? It is more fun to try to develop new tools from scratch than to solve other peoples' already formulated problems! This approach also has its own risks, of course, including total sceptisism from "top people". But see expositions web pages and on my preprint page.
Nov
5
comment A question about the proof of the fact that contractible spaces are simply connected
@Amr: The original aim was to get a theorem which also calculated the fundamental group of the circle, which is, after all, THE basic example in algebraic topology. Notice also that Section 8.4 is used in Section 9.2. The further advantage to me was that it eventually suggested the possibility of higher homotopy van Kampen Theorems, and these allow new calculations in homotopy theory. I also feel maths progresses by getting "neater theorems"! Trying to find why something is true needs the "right" structure. See also Grothendieck's comments on my web page for the book.
Oct
20
awarded  Revival
Oct
15
revised Homology other than singular?
added some more information
Oct
9
revised A question about the proof of the fact that contractible spaces are simply connected
minor
Oct
9
answered A question about the proof of the fact that contractible spaces are simply connected
Sep
29
revised Homology other than singular?
added a comment on cubical methods
Sep
27
comment Should the first be the last by composition of paths?
Philp Higgins book "Categories and Groupoids" downloadable from tac.mta.ca/tac/reprints/articles/7/tr7abs.html consistently uses the "algebraists" convention that functions should be written on the right, as $(x)f$, and then we get a conmposite $fg$ as giving $(x)fg$, first $f$, then $g$. However we are not used to $(x)\sin$. For groupoids and multiple groupoids, I find this convention much better, but have also used the other notation in the same book, writing $G \circ F$ for the composite of functors, first $F$, then $G$. It's a problem!