Superinjective simplicial maps of the two-sided curve complexes on nonorientable surfaces

Branch Point Structure of Covering Maps onto Nonorientable Surfaces

Let /: M -> N be a degree n branched cover onto a compact, connected nonorientable surface with branch points yx, y2.ym in N, and let the multiplicities at points in f~\y¡) be fti, fto • • • > Kv The branching array of/, designated by B, is the following array of numbers: fll'Ml2> • • -«Mi*, /*2i' to • • • » f*2*2 fini' Mm2> • • • ' /Vu We show that the numbers in the branching array must alway...

Ray Tracing of Parametric Surfaces Based on Adaptive Simplicial Complexes

Objects deened by parametric surfaces are a compact representation delivering continuous deened accuracy. For the sake of speed, a discretization towards triangles is inevitable, which can be done adaptively to the projective properties. Simplicial complexes suit perfectly to store the adaptive discretization. Based on adaptive simplicial complexes we propose a modiied ray tracing algorithm. Th...

Close-packed dimers on nonorientable surfaces

Abstract The problem of enumerating dimers on an M×N net embedded on non-orientable surfaces is considered. We solve both the Möbius strip and Klein bottle problems for all M and N with the aid of imaginary dimer weights. The use of imaginary weights simplifies the analysis, and as a result we obtain new compact solutions in the form of double products. The compact expressions also permit us to...

Lyapunov Maps, Simplicial Complexes and the Stone Functor

On Isomorphism of Simplicial Complexes and Their Related Algebras