6,323 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 3 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
20
answered Difference between cellular and simplicial homology
Dec
19
answered What does it mean when people say the co fiber $C_f$ of $f: X\rightarrow Y$ does not dependent on f functorially in homotopy category?
Dec
17
revised How do I prove this using van-Kampen theorem informally ? (2)
page ref inserted
Dec
17
answered How do I prove this using van-Kampen theorem informally ? (2)
Dec
14
answered How can I show $G_0$ and $G_1$ are conjugate subgroups?
Dec
13
comment How can I show $G_0$ and $G_1$ are conjugate subgroups?
Think about how you can use the assumption that $E$ is path-connected and $p(e_0)= p(e_1)=b$!
Dec
12
comment Looking for a homeomorphism $\mathbb{C}P^1 \cong S^2$
I am not sure what text you are using, so I just remark that the projective spaces over the reals, complex numbers and quaternions, are dealt with, including their cell structure, in Ch 5 of my book "Topology and Groupoids".
Dec
10
answered Is mathematics one big tautology?
Dec
10
answered Geometric Homotopy as Chain Homotopy
Dec
10
revised Getting Students to Not Fear Confusion
added some new points
Dec
9
comment Converse to the Eilenberg-Steenrod theorem?
Regarding your "formal construction" you might find my answer to math.stackexchange.com/questions/1055619 relevant. Maybe you are looking for something quite different. I still feel it is worth looking at the history.
Dec
7
answered Original Papers on Singular Homology/Cohomology.
Nov
30
revised Can every basic concept of fundamental group be generalized to homotopy group?
small clarifications
Nov
28
revised Can every basic concept of fundamental group be generalized to homotopy group?
typo and some further explanation of readership
Nov
28
comment Easy papers on fundamental groups (for beginners)
You might try my book "Topology and Groupoids", see pages.bangor.ac.uk/topgpds.html, which is the only text in Englisn to give a van Kampen theorem for the fundamental groupoid on a set of base points, and so obtain the fundamental group of the circle.
Nov
28
answered Can every basic concept of fundamental group be generalized to homotopy group?
Nov
26
comment Is the range of a covering map normal subgroup of codamin?
I like using the idea of covering morphism of groupoids to model covering map of spaces. See mathoverflow.net/questions/159663/functors-and-coverings/… . It leads to the question: given a covering morphism of groupoids $q: H \to \pi_1 X$, when is it realised by $H \cong \pi_1 \widetilde{X}$? See "Topology and Groupoids". A covering morphism is a good algebraic model of a covering map.
Nov
25
answered Are there any disadvantages to working in the category of k-spaces as opposed to Top?
Nov
25
comment Why does a covering map has the injective induced homomorphism?
For an approach using covering morphisms of groupoids see my book "Topology and Groupoids", do a web search for info. This idea has been around since the first 1968 edition. The point is that a covering map is modelled algebraically by a covering morphism.
Nov
17
comment Barratt Whitehead Lemma, Proving exactness at the 'direct sum' module
Does the account in merry.io/resources/algtopIII.pdf help?