4,749 research outputs found
Unstable maps
A map which is non-orientable or has non-empty boundary has a canonical
double cover which is orientable and has empty boundary. The map is called
stable if every automorphism of this cover is a lift of an automorphism of the
map. This note describes several infinite families of unstable maps, and
relates them to similar phenomena for graphs, hypermaps and Klein surfaces.Comment: 11 pages, 4 figure
Enumerating Regular Objects associated with Suzuki Groups
We use the M\"obius function of the simple Suzuki group Sz(q) to enumerate
regular objects such as maps, hypermaps, dessins d'enfants and surface
coverings with automorphism groups isomorphic to Sz(q).Comment: 20 page
Cremona transformations and diffeomorphisms of surfaces
We show that the action of Cremona transformations on the real points of
quadrics exhibits the full complexity of the diffeomorphisms of the sphere, the
torus, and of all non-orientable surfaces. The main result says that if X is
rational, then Aut(X), the group of algebraic automorphisms, is dense in
Diff(X), the group of self-diffeomorphisms of X.Comment: 17 pages, 11 figures, shorter proofs and improvement of the result
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