Full paper in PDF:
$% C. Léger, Opérations sur les cartes et métamorphoses de la catégorie des G-ensembles, Rev. Mat. Univ. Complut. Madrid 4 (1991), no. 1, 4551.%$

Opérations sur les cartes et métamorphoses de la catégorie des G-ensembles

Christian LÉGER
Université Paris 7
U.F.R. de Mathématiques
T. 45-55, 5e etage
2, place Jussieu
75005 Paris France

Received: July 11, 1989
Revised: October 8, 1990
ABSTRACT

We call metamorphosis of a given category an autoequivalence functor. up to within natural equivalence. We show that, given a group G  , the group of metamorphoses of the category of G  -sets (as well as the corresponding group for “sufficiently big” subcategories) may be naturally identified to the group of outer automorphism of G  . We get by this way a natural description of a group of known operations on tessellations of a surface: the identity operation, the Poincaré duality, and four others which generally change the topological type of the surface.

1991 Mathematics Subject Classification: 18A22, 52B70, 51A10.