TY - GEN A1 - Lutz, Frank H. T1 - Enumeration and Random Realization of Triangulated Surfaces N2 - We discuss different approaches for the enumeration of triangulated surfaces. In particular, we enumerate all triangulated surfaces with 9 and 10 vertices. We also show how geometric realizations of orientable surfaces with few vertices can be obtained by choosing coordinates randomly. T3 - ZIB-Report - 06-07 KW - triangulated surfaces KW - polyhedral manifolds Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-9012 ER - TY - GEN A1 - Lutz, Frank H. T1 - Triangulated Manifolds with Few Vertices: Combinatorial Manifolds N2 - In this survey on combinatorial properties of triangulated manifolds we discuss various lower bounds on the number of vertices of simplicial and combinatorial manifolds. Moreover, we give a list of all known examples of vertex-minimal triangulations. T3 - ZIB-Report - 06-08 KW - triangulated manifolds KW - combinatorial properties KW - minimal triangulations Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-9028 ER - TY - GEN A1 - Köhler, Ekkehard G. A1 - Lutz, Frank H. T1 - Triangulated Manifolds with Few Vertices: Vertex-Transitive Triangulations I N2 - We describe an algorithm for the enumeration of (candidates of) vertex-transitive combinatorial $d$-manifolds. With an implementation of our algorithm, we determine, up to combinatorial equivalence, all combinatorial manifolds with a vertex-transitive automorphism group on $n\leq 13$ vertices. With the exception of actions of groups of small order, the enumeration is extended to 14 and 15 vertices. T3 - ZIB-Report - 06-09 KW - triangulated manifolds KW - vertex-transitive triangulations Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-9031 ER - TY - GEN A1 - Csorba, Peter A1 - Lutz, Frank H. T1 - Graph Coloring Manifolds N2 - We introduce a new and rich class of graph coloring manifolds via the Hom complex construction of Lov\´{a}sz. The class comprises examples of Stiefel manifolds, series of spheres and products of spheres, cubical surfaces, as well as examples of Seifert manifolds. Asymptotically, graph coloring manifolds provide examples of highly connected, highly symmetric manifolds. T3 - ZIB-Report - 06-11 KW - graph coloring complexes KW - Hom complexes KW - flag complexes KW - graph coloring manifolds Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-9043 ER - TY - GEN A1 - Hougardy, Stefan A1 - Lutz, Frank H. A1 - Zelke, Mariano T1 - Polyhedra of Genus 2 with 10 Vertices and Minimal Coordinates N2 - We give coordinate-minimal geometric realizations in general position of all 865 vertex-minimal triangulations of the orientable surface of genus 2 in the 4x4x4-cube. T3 - ZIB-Report - 06-12 KW - triangulated surfaces KW - minimal triangulations KW - polyhedral realizations Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-9054 ER - TY - GEN A1 - Hougardy, Stefan A1 - Lutz, Frank H. A1 - Zelke, Mariano T1 - Polyhedra of Genus 3 with 10 Vertices and Minimal Coordinates N2 - We give coordinate-minimal geometric realizations in general position for 17 of the 20 vertex-minimal triangulations of the orientable surface of genus 3 in the 5x5x5-cube. T3 - ZIB-Report - 06-13 KW - triangulated surfaces KW - minimal triangulations KW - polyhedral realizations Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-9064 ER - TY - GEN A1 - Lutz, Frank H. T1 - Combinatorial 3-Manifolds with 10 Vertices N2 - We give a complete enumeration of combinatorial 3-manifolds with 10 vertices: There are precisely 247882 triangulated 3-spheres with 10 vertices as well as 518 vertex-minimal triangulations of the sphere product $S^2 x S^1$ and 615 triangulations of the twisted sphere product $S^2 \underline{x} S^1$. An analysis of the 3-spheres with up to 10 vertices shows that all these spheres are shellable, but that there are 29 vertex-minimal non-shellable 3-balls with 9 vertices. T3 - ZIB-Report - 06-14 KW - triangulated manifolds KW - enumeration KW - minimal triangulations KW - shellability Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-9071 ER - TY - GEN A1 - Lutz, Frank H. T1 - Triangulated Manifolds with Few Vertices: Geometric 3-Manifolds N2 - We explicitly construct small triangulations for a number of well-known $3$-dimensional manifolds and give a brief outline of some aspects of the underlying theory of $3$-manifolds and its historical development. T3 - ZIB-Report - 03-36 KW - triangulating manifolds KW - 3-manifolds KW - geometrization conjecture KW - 3-dimensional geometries KW - Seifert manifolds KW - torus bundles Y1 - 2003 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7583 ER - TY - GEN A1 - Lutz, Frank H. T1 - Small Examples of Non-Constructible Simplicial Balls and Spheres N2 - We construct non-constructible simplicial $d$-spheres with $d+10$ vertices and non-constructible, non-realizable simplicial $d$-balls with $d+9$ vertices for $d\geq 3$. T3 - ZIB-Report - 03-28 KW - simplicial balls and spheres KW - constructibility KW - shellability KW - vertex-decomposability KW - knots in 3-balls and 3-spheres Y1 - 2003 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7500 ER - TY - GEN A1 - Joswig, Michael A1 - Lutz, Frank H. T1 - One-Point Suspensions and Wreath Products of Polytopes and Spheres N2 - It is known that the suspension of a simplicial complex can be realized with only one additional point. Suitable iterations of this construction generate highly symmetric simplicial complexes with a various interesting combinatorial and topological properties. In particular, infinitely many non-PL spheres as well as contactible simplicial complexes with a vertex-transitive group of automorphisms cab be contained in this way. T3 - ZIB-Report - 04-08 KW - dual wedge KW - suspension KW - wreath product KW - shellability KW - Z-acyclic complexes KW - non-PL spheres KW - Hirsch conjecture Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7836 ER - TY - GEN A1 - Lutz, Frank H. T1 - Triangulated Manifolds with Few Vertices: Centrally Symmetric Spheres and Products of Spheres N2 - The aim of this paper is to give a survey of the known results concerning centrally symmetric polytopes, spheres, and manifolds. We further enumerate nearly neighborly centrally symmetric spheres and centrally symmetric products of spheres with dihedral or cyclic symmetry on few vertices, and we present an infinite series of vertex-transitive nearly neighborly centrally symmetric 3-spheres. T3 - ZIB-Report - 04-11 KW - centrally symmetric polytopes KW - crosspolytope KW - combinatorial manifolds KW - products of spheres Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7863 ER -