6,318 reputation
11321
bio website bangor.ac.uk/r.brown
location University of Wales-Bangor, United Kingdom
age 79
visits member for 2 years, 8 months
seen 5 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!


Jan
9
answered Good source for a point set topological introduction to CW complexes?
Jan
8
answered Can torsion in the fundamental group happen in “the real world”
Jan
7
revised Dunce Cap triangle homotopy equivalent to $S^1$
added pictures
Jan
7
revised Failure of excision for $\pi_2$
typo
Jan
7
revised Failure of excision for $\pi_2$
added on nonabelian tensor product
Jan
6
answered Dunce Cap triangle homotopy equivalent to $S^1$
Jan
5
revised Failure of excision for $\pi_2$
addition on Relkative Hurewicz Theorem
Jan
3
answered Path Connectedness in Van Kampen Theorem
Jan
2
comment A question about the proof of the fact that contractible spaces are simply connected
@Amr: The answer is: Very much so! See math.stackexchange.com/questions/617018/… for an application, and also for links to the full theory. Further developments are also in my papers with Jean-Louis Loday , [42, 49, 51] on my publication list. The most popular consequence of [49], and [52], are listed in pages.bangor.ac.uk/~mas010/nonabtens.html . Other texts in topology don't seem to like the words "higher van Kampen Theorem", it seems, though the first such, in dimension 2, was published in 1978.
Jan
2
comment Generalisation of Seifert-van Kampen theorem?
@Stefan: Please try now! My mistake.
Jan
1
revised Generalisation of Seifert-van Kampen theorem?
typo
Jan
1
answered Generalisation of Seifert-van Kampen theorem?
Dec
31
comment Generalisation of Seifert-van Kampen theorem?
A further comment on our paper is that the proof goes by a direct verification of the universal property, rather than any specific description of colimits in groupoids. An advantage of groupoids is that the coproduct in the category of groupoids is just disjoint union. The further advantage of this type of proof is that it generalises to higher dimensions, yielding new results on for example excision for second relative homotopy groups, see an answer of mine on this site.
Dec
31
comment Generalisation of Seifert-van Kampen theorem?
[1]:pages.bangor.ac.uk/~mas010/publicfull.htm The most general result of this kind involving fundamental groupoids on a set of base points is in R. Brown and A. Razak, "A van Kampen theorem for unions of non-connected spaces", Archiv. Math. 42 (1984) 85-88, item [41] on my [publication list][1].
Dec
31
revised Failure of excision for $\pi_2$
added a relatio to work of Blakers and massey
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 $X$