Multiple residues in dimension three

Abstract Edge-coloured graphs can be seen as schemes of pseudosimplicial complexes. Standard manipulation of such graphs may introduce unwanted singularities in the represented complexes. Here, a technique of elimination for a large class of singularities in four-colored graphs (hence in 3-dimensional complexes) is presented.

[1]  M. Ferri,et al.  A CHARACTERIZATION OF PUNCTURED $n$ -SPHERES , 1985 .

[2]  C. Wall On Simply-Connected 4-Manifolds , 1964 .

[3]  C. Rourke,et al.  Introduction to Piecewise-Linear Topology , 1972 .

[4]  Carlo Gagliardi,et al.  Extending the concept of genus to dimension $n$ , 1981 .

[5]  Alberto Cavicchioli,et al.  Su una decomposizione normale per le n-varietà chiuse , 1980 .

[6]  Javier Bracho,et al.  The combinatorics of colored triangulations of manifolds , 1987 .

[7]  Andrew Vince Graphic matroids, shellability and the Poincare Conjecture , 1983 .

[8]  Sóstenes Lins,et al.  Graph-encoded 3-manifolds , 1985, Discret. Math..

[9]  Andrew Vince A Non-Shellable 3-Sphere , 1985, Eur. J. Comb..

[10]  Carlo Gagliardi,et al.  A graph-theoretical representation of PL-manifolds — A survey on crystallizations , 1986 .

[11]  Carlo Gagliardi,et al.  A combinatorial characterization of 3-manifold crystallizations , 1979 .

[12]  Carlo Gagliardi,et al.  Cobordant crystallizations , 1983, Discret. Math..

[13]  Carlo Gagliardi,et al.  The only genus zero n-manifold is S^n , 1982 .

[14]  Sóstenes Lins Graph-encoded maps , 1982, J. Comb. Theory, Ser. B.

[15]  Bojan Mohar,et al.  Simplicial schemes , 1987, J. Comb. Theory, Ser. B.

[16]  Carlo Gagliardi,et al.  Crystallizations of PL-manifolds with connected boundary , 1980 .

[17]  Carlo Gagliardi,et al.  Regular imbeddings of edge-coloured graphs , 1981 .

[18]  Frank Harary,et al.  Graph Theory , 2016 .

[19]  C. Gagliardi Regular genus: The boundary case , 1987 .