bio | website | bangor.ac.uk/r.brown |
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location | ||
age | 80 | |
visits | member for | 4 years, 11 months |
seen | 8 hours ago | |
stats | profile views | 4,284 |
As a result of giving courses at BSc and MSc level at Liverpool, I got involved in writing a text published as "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 with Chris Spencer (1971-73), Philip Higgins (1974-2005), and Jean-Louis Loday (1981-1985), and excellent contributions from research students.
Since 2001 I was engaged in writing a Tract giving an exposition in one place of my work since 1974 with Philip Higgins and a number of others on (strict) higher homotopy groupoids and their applications. A first step was to make available my out of print book on Topology, and this was made available in 2006 under the title "Topology and Groupoids" see my web page. The higher dimensional work was published in August, 2011, as a European Mathematical Society Tract, Vol 15, under the title "Nonabelian algebraic topology: filtered spaces, crossed complexes, cubical homotopy groupoids" with co-authors P.J. Higgins and R. Sivera.
Mar 30 |
revised |
Has any attempt been made to classify finite groupoids?
typo and word order |
Mar 30 |
comment |
Has any attempt been made to classify finite groupoids?
@Qiaochu Yuan: Groupoids equipped with a $G$-action where $G$ is a group occur in the study of orbit spaces, where the groupoid is the fundamental groupoid $\pi_1(X)$. See Chapter 11 of Topology and Groupoids, where the "orbit groupoid" is related to the fundamental groupoid of the orbit space! |
Mar 29 |
revised |
Has any attempt been made to classify finite groupoids?
typo |
Mar 29 |
awarded | Necromancer |
Mar 27 |
revised |
Has any attempt been made to classify finite groupoids?
added extra comments |
Mar 25 |
revised |
What's special about the Simplex category?
added some extra references |
Mar 24 |
revised |
What's special about the Simplex category?
more info on motives and cubical sets |
Mar 16 |
comment |
Brandt's definition of groupoids (1926)
One of the fascinations of mathematics is how structures can be appropriate to help us understand the small and the large. A good example is monoidal categories which crop up for describing the family of braid groups and also of chain complexes. Charles Ehresmann wrote that his aim was to understand the structure of everything; that also includes the structure of structures! |
Mar 14 |
comment |
Brandt's definition of groupoids (1926)
Martin writes "groupoids look very much like groups except that the product is only defined partially.". My definition of "higher dimensional algebra" is "the study of algebraic structures with partially defined operations whose domains are determined by geometric conditions", so that we can combine algebra and geometry, opening new worlds. Philip Higgins wrote the first paper on partial algebraic structures, "Algebras with a scheme of operators", Math. Nachr. 27 (1963) 115--132. |
Mar 14 |
comment |
Brandt's definition of groupoids (1926)
It is not unusual for people to be influenced by a work and then forget about that as they write and rewrite. I have probably done this. |
Mar 14 |
comment |
Brandt's definition of groupoids (1926)
I have no explanation. The paper listed under General Papers no 8 at people.math.ethz.ch/~knus/publications09.html states that it is believed that the groupoid axioms influenced the work of Eilenberg and Mac Lane. |
Mar 14 |
revised |
Brandt's definition of groupoids (1926)
added a reference to a translation of the Reidemeister book |
Mar 13 |
answered | Brandt's definition of groupoids (1926) |
Mar 12 |
comment |
Dimension leaking in homology as opposed to homotopy
@AlexDegty: The groupoid version of the SvKT using a set of base points which I published in 1967 gets over the path-connected assumption - see the presentation referred to in my answer, and mathoverflow.net/questions/40945/… |
Mar 12 |
revised |
Dimension leaking in homology as opposed to homotopy
slight clarification |
Mar 12 |
answered | Dimension leaking in homology as opposed to homotopy |
Mar 11 |
revised |
Compelling evidence that two basepoints are better than one
grammatical improvement to last sentence |
Mar 11 |
awarded | Necromancer |
Mar 11 |
revised |
Compelling evidence that two basepoints are better than one
added another link |
Mar 7 |
answered | Topological Grothendieck Construction |