LisMath Seminar 

22/05/2015, 16:00 — 17:00 — Room B3-01, Interdisciplinary Complex, Universidade de Lisboa
Juan Quijano, LisMath Programme, Universidade de Lisboa.

A brief introduction to groupoids.

Groupoids were introduced by Brandt in his 1926 paper [1] and since then they have been used in a wide variety of areas of mathematics, from ergodic theory and functional analysis to homotopy theory, algebraic geometry, differential geometry, differential topology and group theory. Specially in category theory and homotopy theory, a groupoid generalises the notion of group in several equivalent ways: A groupoid can be seen as a group with a partial function replacing the binary operation or a category in which every morphism is invertible. In this talk, going through the notion of symmetry, I would like to justify the argument that the theory of groupoids does not differ widely in spirit and aims from the theory of groups and how groupoids describe symmetry. Of course, I will give the basic definitions and important examples in a wide range.

Bibliography:

[1] H. Brandt, Ueber eine Verallgemeinerung des Gruppenbegriffes, Math. Ann. 96, 360- 366 (1926).

[2] R. Brown, From Groups to Groupoids: A Brief Survey, Bull. London Math. Soc. 19, 113-134 (1987).

[3]A. Weinstein, Groupoids: Unifying Internal and External Symmetry, Notices Amer. Math. Soc. 43 (1996).

See also

juanpablo_groupoidsv1.pdf