5,770 reputation
11321
bio website bangor.ac.uk/r.brown
location University of Wales-Bangor, United Kingdom
age 79
visits member for 2 years, 5 months
seen 11 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!


14h
comment Fundamental group of some disk quotient
I am sorry this has been closed, although the question is not all that well phrased. It seems to me that the question is about the orbit space of the action by rotation through $\pi/2$ of the cyclic group $C_4$ of order $4$ on the disc $D^2$. The general question is calculating the fundamental group of the action say of a finite group $G$ on a CW-complex $X$. I can explain what techniques are available, given space for an answer. The standard books deal only with the case of free actions, when covering space methods are adequate.
1d
awarded  soft-question
1d
revised Explaining what is Pathwise-connectedness.
typo
1d
answered Explaining what is Pathwise-connectedness.
Sep
18
answered Homeomorphic, homotopy equivalent and deformation retracts. How do I get a feeling for this?
Sep
16
answered What is the universal cover of a discrete set?
Sep
14
awarded  Fanatic
Sep
13
revised Obtaining Wirtinger presentation using van Kampen theorem
typo
Sep
13
answered Obtaining Wirtinger presentation using van Kampen theorem
Sep
12
comment Fundamental crossed square of a square of spaces
That looks right. You might find the following helpful: R. Steiner, Resolutions of spaces by n-cubes of fibrations, J. London Math. Soc. (2) 34 (1986) 169-176. You may need: "An introduction to homotopy theory and duality I" WH Cockroft, TM Jarvis - Bull. Soc. Math. Belgique, 1964
Sep
11
answered Fundamental crossed square of a square of spaces
Sep
6
answered Any relations between the weak topology on a Banach Space and the weak topology on CW complexes?
Sep
6
comment Maps from cogroups to groups & Eckmann-Hilton
Just a comment to say that you have to be working in the category of pointed spaces and homotopies respecting base point.
Sep
3
comment Identification of points versus line drawn between points
It does not matter if the line is inside or outside, the two are homeomorphic! Anyway, the map from the right hand picture to the left hand picture which collapses the outside bit is a homotopy equivalence, so induces an isomorphism of fundamental groups. They both have fundamental group the integers, as for the circle.
Sep
3
answered More elementary proof that $\pi_n(S^n) \cong \mathbb{Z}$
Sep
3
answered Identification of points versus line drawn between points
Sep
3
revised Suggestion about Algebraic Topology talk
gave another link
Aug
25
revised Isomorphism of Fundamental Groups (arcwise connected)
typos
Aug
24
answered Isomorphism of Fundamental Groups (arcwise connected)
Aug
18
comment The nature of isomorphism between fundamental groups with different base points
This question confirms my view that a lack of a groupoidal approach to 1-dimensional homotopy theory easily leads to confusion. This groupoid approach has been advocated by me since 1968, see my web pages.