Restricting valence for polyhedral surfaces and manifolds

• Applicant: Professor John M. Sullivan, Ph.D.
• Subject Area: Mathematics
• Term: from 2005 to 2012
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 5471407

The construction of a combinatorial manifold, from simplices or other polyhedral facets, is largely determined by the valence - how many facets fit around each face of codimension two. Valence, and the restrictions one can place on it, is a common theme uniting the several parts of this project.We had the opportunity to appoint Dr. Frank Lutz, a postdoc with a wellestablished research program, to work on the project in the first funding period. Thus the emphasis of the work, as described here, changed substantially from the initial proposal.Our work on the project during the first funding period, as well as our planned work during the next period, can be divided into several parts:Simplicial manifolds of small valence, Quadrangulations with high valence and equivelar surfaces, Higher-dimensional soap films, Realizability in a given isotopy class.

• DFG Programme: Research Units
• Subproject of: FOR 565: Polyhedral Surfaces