| bio | website | bangor.ac.uk/r.brown |
|---|---|---|
| location | University of Wales-Bangor, United Kingdom | |
| age | 78 | |
| visits | member for | 1 year, 1 month |
| seen | May 19 at 14:39 | |
| stats | profile views | 531 |
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 mew 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!
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May 16 |
revised |
A question about Non-Abelian Tensor Product clarified a reference, and added a comment |
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May 7 |
comment |
What makes a good mathematician? Trying to find out why things are true. Looking for understanding. |
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May 2 |
comment |
details and reference (for undergraduate student) on the constructions and topology of $\mathbb{RP}^n$ @Ric: The cell structure in this exposition is just one of the properties deduced from the general view of projective spaces over the reals, complex numbers and quaternions. You could compare T&G with Porteous "Topological Geometry". |
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Apr 26 |
answered | Proofs for Undergraduates |
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Apr 25 |
answered | Conjugacy classes in the fundamental group |
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Apr 25 |
answered | details and reference (for undergraduate student) on the constructions and topology of $\mathbb{RP}^n$ |
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Apr 22 |
answered | Connected groupoids and action groupoids |
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Apr 8 |
comment |
Join, Smash Product and Disjoint Union of Tori Of course the term $rx+ty$ should be $rx+sy$. The idea is that the join of two disjoint subsets $X,Y$ of a high dim real vector space consists of all line segments joining points of $X$ to points of $Y$, where $X,Y$ are in such general position that the line segments joining them do not meet. The last condition is clumsy so one writes down the formal definition, and the initial topology gives nice properties such as associativity. |
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Apr 8 |
awarded | Yearling |
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Apr 8 |
comment |
Join, Smash Product and Disjoint Union of Tori Just a small comment: join is not distributive with disjoint union since the join of a singleton with a doubleton is connected. For your pictures, it could be helpful to consider $X * Y$ as consisting of formal sums $rx+ty$ where $x \in X, y \in y, 0 \leqslant r,s \leqslant 1, r+s=1$ and of course $0x+1y=y, 1x+0y=x$. A convenient topology on the join is often the initial topology, see my book "Topology and Groupoids". |
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Apr 1 |
comment |
Representation theorems for groups My answer to mathoverflow.net/questions/126074/anick-resolution is relevant to the algorithmic aspects of the process Jim describes in the last paragraph of his answer. Graham Ellis formulates this process as starting with the $2$-complex $K$ of the presentation, Graham Ellis constructs inductively a universal cover of an Eilenberg-Mac Lane complex together with a contracting homotopy, and this is programmed in GAP. |
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Mar 31 |
awarded | Good Answer |
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Mar 31 |
revised |
does torus have boundary? And the concept of boundary typos |
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Mar 31 |
answered | does torus have boundary? And the concept of boundary |
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Mar 28 |
answered | Visualizing $E=Y\cap G$ geometrically for some open set $G\subset X$ |
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Mar 23 |
awarded | Nice Answer |
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Mar 1 |
revised |
Compact sets in Hausdorff spaces. added some comments on methodology |
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Feb 24 |
comment |
Compact sets in Hausdorff spaces. @Brian: Some of us like to see the utility of a general result in terms of its corollaries. It is a matter of personal taste, perhaps. |
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Feb 23 |
answered | Compact sets in Hausdorff spaces. |
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Feb 21 |
answered | abstract algebra recommended book |