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Polyhedral surfaces of high genus
Günter M. Ziegler
The construction of the COMBINATORIAL data for a surface with n vertices of maximal genus is a classical problem: The maximal genus g=[(n-3)(n-4)/12] was achieved in the famous ``M…
Convex Polytopes: Extremal Constructions and f-Vector Shapes
Günter M. Ziegler
These lecture notes treat some current aspects of two closely interrelated topics from the theory of convex polytopes: the shapes of f-vectors, and extremal constructions. The firs…
The Topological Tverberg Problem and winding numbers
Torsten Schöneborn, Günter M. Ziegler
The Topological Tverberg Theorem claims that any continuous map of a (q-1)(d+1)-simplex to \R^d identifies points from q disjoint faces. (This has been proved for affine maps, for…
Projected Products of Polytopes
Günter M. Ziegler
We construct a 2-parameter family of 4-dimensional polytopes with extreme combinatorial structure: In this family, the ``fatness'' of the f-vector gets arbitrarily close to 9, the…