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1) We introduce random discrete Morse theory as a computational scheme to measure the complicatedness of a triangulation.
Die beiden Dodekaederräume
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Non-simplicially collapsible triangulations of I n I^{n}
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The triangulations of the 3 3 -sphere with up to 8 8 vertices
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The topology of four-dimensional manifolds
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The 9 9 -vertex complex projective plane
W. Kühnel and T. F. Banchoff · 1983
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Heegaard genus of closed orientable Seifert 3 3 -manifolds
M. Boileau and H. Zieschang · 1984
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A topological approach to evasiveness
J. Kahn, M. Saks, and D. Sturtevant · 1984
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Some closed 4 4 -manifolds with exotic differentiable structure
M. Kreck · 1984
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A potential smooth counterexample in dimension 4 4 to the Poincaré conjecture, the Schoenflies conjecture, and the Andrews–Curtis conjecture
S. Akbulut and R. Kirby · 1985
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Minimal triangulations of Kummer varieties
W. Kühnel · 1987
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Konstruktionsmethoden und das kombinatorische Homöomorphieproblem für Triangulationen kompakter semilinearer Mannigfaltigkeiten
U. Pachner · 1987
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Unshellable triangulations of spheres
W. B. R. Lickorish · 1991
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15 15 -vertex triangulations of an 8 8 -manifold
U. Brehm and W. Kühnel · 1992
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Neighborly 2 2 -manifolds with 12 12 vertices
A. Altshuler, J. Bokowski, and P. Schuchert · 1996
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Morse theory for cell complexes
R. Forman · 1998
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Triangulated Manifolds with Few Vertices and Vertex-Transitive Group Actions
F. H. Lutz · 1999
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Constructions preserving evasiveness and collapsibility
V. Welker · 1999
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Simplicial manifolds, bistellar flips and a 16 16 -vertex triangulation of the Poincaré homology 3 3 -sphere
A. Björner and F. H. Lutz · 2000
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On discrete Morse functions and combinatorial decompositions
M. K. Chari · 2000
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A triangulated K3 surface with the minimum number of vertices
M. Casella and W. Kühnel · 2001
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A user’s guide to discrete Morse theory
R. Forman · 2002
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Computing the face lattice of a polytope from its vertex-facet incidences
V. Kaibel and M. E. Pfetsch · 2002
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Examples of ℤ \mathbb{Z} -acyclic and contractible vertex-homogeneous simplicial complexes
F. H. Lutz · 2002
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A 16 16 -vertex triangulation of the Poincaré homology 3 3 -sphere and non-PL spheres with few vertices
A. Björner and F. H. Lutz · 2003
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Collapsing a simplex to a noncollapsible simplicial complex
K. Crowley, A. Ebin, H. Kahn, P. Reyfman, J. White, and M. Xue · 2003
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Finite covers of random 3 3 -manifolds
N. M. Dunfield and W. P. Thurston · 2006
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Computing optimal Morse matchings
M. Joswig and M. E. Pfetsch · 2006
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Homological connectivity of random 2 2 -complexes
N. Linial and R. Meshulam · 2006
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GAP — Groups, Algorithms, and Programming, Version 4.4.12
The GAP Group · 2008
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Combinatorial 3 3 -manifolds with 10 10 vertices
F. H. Lutz · 2008
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Discrete Morse functions from Fourier transforms
A. Engström · 2009
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f f -vectors of 3 3 -manifolds
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Some algorithmic problems in polytope theory
V. Kaibel and M. E. Pfetsch · 2003
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Optimal discrete Morse functions for 2 2 -manifolds
T. Lewiner, H. Lopes, and G. Tavares · 2003
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Toward optimality in discrete Morse theory
T. Lewiner, H. Lopes, and G. Tavares · 2003
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A vertex-minimal non-shellable simplicial 3 3 -ball with 9 9 vertices and 18 18 facets
F. H. Lutz · 2003
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Triangulated Manifolds with Few Vertices: Geometric 3 3 -Manifolds
F. H. Lutz · 2003
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BISTELLAR
F. H. Lutz · 2003
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F. H. Lutz · 2009
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Isomorphism free lexicographic enumeration of triangulated surfaces and 3 3 -manifolds
T. Sulanke and F. H. Lutz · 2009
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Exotic smooth structures on small 4 4 -manifolds with odd signatures
A. Akhmedov and B. D. Park · 2010
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The fundamental group of random 2 2 -complexes
E. Babson, C. Hoffman, and M. Kahle · 2010
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Sum complexes—a new family of hypertrees
N. Linial, R. Meshulam, and M. Rosenthal · 2010
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Differential topology forty-six years later
J. Milnor · 2011
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Combinatorial properties of the K 3 K3 surface: Simplicial blowups and slicings
J. Spreer and W. Kühnel · 2011
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Discrete Morse theory for manifolds with boundary
B. Benedetti · 2012
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Topology of random 2 2 -complexes
D. Cohen, A. Costa, M. Farber, and T. Kappeler · 2012
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Combinatorial Morse flows are hard to find
L. I. Nicolaescu · 2012
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Recognition of collapsible complexes is NP-complete
M. Tancer · 2012
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Collapsibility and vanishing of top homology in random simplicial complexes
L. Aronshtam, N. Linial, T. Łuczak, and R. Meshulam · 2013
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Smoothing discrete Morse theory
B. Benedetti · 2013
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Knots in collapsible and non-collapsible balls
B. Benedetti · 2013
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The dunce hat and a minimal non-extendably collapsible 3 3 -ball
B. Benedetti · 2013
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Library of triangulations, 2013
B. Benedetti · 2013
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Constructing complicated spheres
M. Tsuruga and F. H. Lutz · 2013
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