Applet: Surface of genus 2.

Applet: Surface of genus 2.

Priv.-Doz. Dr. Frank H. Lutz

Phone:	+49-30-314-29257
Fax:	+49-30-314-29260
Email:	lutzmath.tu-berlin.de
Room:	MA 307

Research Interests

• Combinatorial & Computational Topology
• Triangulations of Manifolds
• Algebraic Topology
• Topological Combinatorics
• Optimization
• Visualization of Topological Spaces
• Polyhedral Surfaces
• Combinatorial Geometry
• History of Geometry and Topology

Teaching

Papers and Preprints

• Wolfgang Kühnel and Frank H. Lutz.   A census of tight triangulations.   Periodica Math. Hung. 39, 161-183 (1999).
• Anders Björner and Frank H. Lutz.   Simplicial manifolds, bistellar flips and a 16-vertex triangulation of the Poincaré homology 3-sphere.   Exp. Math. 9, 275-289 (2000).
• Frank H. Lutz.   Some results related to the Evasiveness Conjecture.   J. Comb. Theory, Ser. B 81, 110-124 (2001).
• Frank H. Lutz.   Examples of Z-acyclic and contractible vertex-homogeneous simplicial complexes.   Discrete Comput. Geom. 27, 137-154 (2002).
• Frank H. Lutz.   Small examples of non-constructible simplicial balls and spheres.   SIAM J. Discrete Math. 18, 103-109 (2004).
• Michael Joswig and Frank H. Lutz.   One-point suspensions and wreath products of polytopes and spheres.   J. Comb. Theory, Ser. A 110, 193-216 (2005).
• Péter Csorba and Frank H. Lutz.   Graph coloring manifolds.   Algebraic and Geometric Combinatorics, Euroconf. Math., Anogia, Crete, Greece, 2005 (C. A. Athanasiadis, V. V. Batyrev, D. I. Dais, M. Henk, and F. Santos, eds.). Contemporary Mathematics 423, 51-69. American Mathematical Society, Providence, RI, 2006.
• Frank H. Lutz.   Enumeration and random realization of triangulated surfaces.   Discrete Differential Geometry (A. I. Bobenko, P. Schröder, J. M. Sullivan, and G. M. Ziegler, eds.). Oberwolfach Seminars 38, 235-253. Birkhäuser, Basel, 2008.
• Frank H. Lutz.   Combinatorial 3-manifolds with 10 vertices.   Beitr. Algebra Geom. 49, 97-106 (2008).
• Frank H. Lutz, Thom Sulanke, and Ed Swartz.   f-vectors of 3-manifolds.   Electron. J. Comb. 16, No. 2, Research Paper R13, 33 p. (2009).
• Thom Sulanke and Frank H. Lutz.   Isomorphism-free lexicographic enumeration of triangulated surfaces and 3-manifolds.   Eur. J. Comb. 30, 1965-1979 (2009).
• Stefan Hougardy, Frank H. Lutz, and Mariano Zelke.   Surface realization with the intersection segment functional.   Exp. Math. 19, 79-92 (2010).
• Frank H. Lutz and Nikolaus Witte.   Knotted polyhedral tori.   Preprint, 10 pages, 2007; arXiv:0707.1281.
• Frank H. Lutz, Thom Sulanke, Anand K. Tiwari, and Ashish K. Upadhyay.   Equivelar and d-covered triangulations of surfaces. I.   Preprint, 21 pages, 2010; arXiv:1001.2777.
• Frank H. Lutz.   Equivelar and d-covered triangulations of surfaces. II. Cyclic triangulations and tessellations.   Preprint, 27 pages, 2010; arXiv:1001.2779.

• Frank H. Lutz.   Triangulated Manifolds with Few Vertices and Vertex-Transitive Group Actions.   Dissertation.   Shaker Verlag, Aachen, 1999.

Electronic Geometry Models

• Frank H. Lutz.   Császár's Torus.   Electronic Geometry Models, No. 2001.02.069 (2002).
• Anders Björner and Frank H. Lutz.   A 16-vertex triangulation of the Poincaré homology 3-sphere and non-PL spheres with few vertices.   Electronic Geometry Models, No. 2003.04.001 (2003).
• Frank H. Lutz.   A vertex-minimal non-shellable simplicial 3-ball with 9 vertices and 18 facets.   Electronic Geometry Models, No. 2003.05.004 (2004).
• Frank H. Lutz.   Vertex-minimal not vertex-decomposable balls.   Electronic Geometry Models, No. 2003.06.001 (2004).
• Stefan Hougardy, Frank H. Lutz, and Mariano Zelke.   Polyhedra of genus 2 with 10 vertices and minimal coordinates.   Electronic Geometry Models, No. 2005.08.001 (2007).
• Stefan Hougardy, Frank H. Lutz, and Mariano Zelke.   Polyhedra of genus 3 with 10 vertices and minimal coordinates.   Electronic Geometry Models, No. 2006.02.001 (2007).
• Stefan Hougardy, Frank H. Lutz, and Mariano Zelke.   Polyhedral tori with minimal integer coordinates.   Electronic Geometry Models, No. 2008.10.001 (2008).
• Frank H. Lutz and Günter M. Ziegler.   A small polyhedral Z-acyclic 2-complex in R4.   Electronic Geometry Models, No. 2008.11.001 (2008).
• Bruno Benedetti and Frank H. Lutz.   The dunce hat and a minimal non-extendably collapsible 3-ball.   Preprint, 7 pages, 2009; arXiv:0912.3723.

Extended Abstracts

• Frank H. Lutz.   Triangulated surfaces and higher-dimensional manifolds.   Oberwolfach Reports 3, No. 1, 706-707 (2006).
• Frank H. Lutz.   Periodic foams and simplicial manifolds with small valence.   Oberwolfach Reports 4, No. 1, 228-230 (2007).

The Manifold Page

Book

• Frank H. Lutz.   Triangulated Manifolds.   Springer-Verlag, to appear   (with contributions by Anders Björner, Michael Joswig, Volker Kaibel, Ekkehard Köhler, Wolfgang Kühnel, Arnold Waßmer).

• Michael Joswig.   Computing Invariants of Simplicial Manifolds.   Preprint, 13 pages, 2004; arXiv:math/0401176.
• Frank H. Lutz.   Triangulated Manifolds with Few Vertices: Geometric 3-Manifolds.   Preprint, 48 pages, 2003; arXiv:math/0311116.
• Frank H. Lutz.   Triangulated Manifolds with Few Vertices: Centrally Symmetric Spheres and Products of Spheres.   Preprint, 26 pages, 2004; arXiv:math/0404465.
• Frank H. Lutz.   Triangulated Manifolds with Few Vertices: Combinatorial Manifolds.   Preprint, 37 pages, 2005; arXiv:math/0506372.
• Ekkehard G. Köhler and Frank H. Lutz.   Triangulated Manifolds with Few Vertices: Vertex-Transitive Triangulations I.   Preprint, 74 pages, 2005; arXiv:math/0506520.

Schnellkurs Ingenieurmathematik

• TU intern:  Aus drei mach eins: Schnellkurs Mathematik für Ingenieure.

• Frank H. Lutz und Brigitte Lutz-Westphal.   Schnellkurs Ingenieurmathematik - Pilotprojekt an der TU Berlin.   DMV-Mitteilungen 3/2005, 188-191.

Topological Software (in GAP)

• BISTELLAR (Version Nov/2003): heuristics to reduce the size of a given triangulated manifold; it can be used to recognize combinatorial d-spheres and therefore to test whether a pure simplicial complex is a combinatorial manifold.

• BISTELLAR_EQUIVALENT (Version Feb/1999)

• FundamentalGroup (Version Nov/2003): routine to compute a ``small´´ presentation of the fundamental group of a finite simplicial complex.

• MANIFOLD_VT (Version Apr/2002)

• SEIFERT (Version Nov/2003): produces triangulations of all Seifert manifolds.

Last modified: Mon May 10 17:44:12 CEST 2010