Results 1  10
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912
Discrete Morse Theory for Manifolds with Boundary
, 2012
"... We introduce a version of discrete Morse theory specific for manifolds with boundary. The idea is to consider Morse functions for which all boundary cells are critical. We obtain “Relative Morse Inequalities ” relating the homology of the manifold to the number of interior critical cells. We also ..."
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Cited by 14 (8 self)
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subdivision of any simplicial constructible dball is
Small examples of nonconstructible simplicial balls and spheres
 SIAM J. Discrete Math
, 2004
"... We construct nonconstructible simplicial dspheres with d + 10 vertices and nonconstructible, nonrealizable simplicial dballs with d + 9 vertices for d≥3. 1 ..."
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Cited by 14 (6 self)
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We construct nonconstructible simplicial dspheres with d + 10 vertices and nonconstructible, nonrealizable simplicial dballs with d + 9 vertices for d≥3. 1
A Moore bound for simplicial complexes
 BULL. LONDON MATH. SOC
"... Let X be a ddimensional simplicial complex with N faces of dimension (d − 1). Suppose that any (d − 1)face of X is contained in at least k ≥ d+ 2 faces of X of dimension d. Extending the classical Moore bound for graphs, it is shown that X must contain a ball B of radius at most dlogk−dNe such th ..."
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Cited by 9 (2 self)
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Let X be a ddimensional simplicial complex with N faces of dimension (d − 1). Suppose that any (d − 1)face of X is contained in at least k ≥ d+ 2 faces of X of dimension d. Extending the classical Moore bound for graphs, it is shown that X must contain a ball B of radius at most dlogk−d
Hypercovers and simplicial presheaves
, 2004
"... We use hypercovers to study the homotopy theory of simplicial presheaves. The main result says that model structures for simplicial presheaves involving local weak equivalences can be constructed by localizing at the hypercovers. One consequence is that the fibrant objects can be explicitly describe ..."
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Cited by 62 (6 self)
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We use hypercovers to study the homotopy theory of simplicial presheaves. The main result says that model structures for simplicial presheaves involving local weak equivalences can be constructed by localizing at the hypercovers. One consequence is that the fibrant objects can be explicitly
On locally constructible spheres and balls
, 2009
"... Durhuus and Jonsson (1995) introduced the class of “locally constructible ” (LC) 3spheres and showed that there are only exponentiallymany combinatorial types of simplicial LC 3spheres. Such upper bounds are crucial for the convergence of models for 3D quantum gravity. We characterize the LC prop ..."
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Cited by 14 (8 self)
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property for dspheres (“the sphere minus a facet collapses to a (d − 2)complex”) and for dballs. In particular, we link it to the classical notions of collapsibility, shellability and constructibility, and obtain hierarchies of such properties for simplicial balls and spheres. The main corollaries from
Decompositions of Simplicial Balls and Spheres With Knots Consisting of Few Edges
, 1999
"... Constructibility is a condition on pure simplicial complexes that is weaker than shellability. In this paper we show that nonconstructible triangulations of the ddimensional sphere exist for every d 3. This answers a question of Danaraj & Klee [8]; it also strengthens a result of Lickorish [1 ..."
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Cited by 19 (5 self)
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Constructibility is a condition on pure simplicial complexes that is weaker than shellability. In this paper we show that nonconstructible triangulations of the ddimensional sphere exist for every d 3. This answers a question of Danaraj & Klee [8]; it also strengthens a result of Lickorish
Simplicial Approximation
, 2004
"... This paper displays an approach to the construction of the homotopy theory of simplicial sets and the corresponding equivalence with the homotopy theory of topological spaces which is based on simplicial approximation techniques. The required simplicial approximation results for simplicial sets and ..."
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Cited by 9 (3 self)
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This paper displays an approach to the construction of the homotopy theory of simplicial sets and the corresponding equivalence with the homotopy theory of topological spaces which is based on simplicial approximation techniques. The required simplicial approximation results for simplicial sets
CONSTRUCTING SIMPLICIAL BRANCHED COVERS
, 2007
"... Branched covers are applied frequently in topology most prominently in the construction of closed oriented PL dmanifolds. In particular, strong bounds for the number of sheets and the topology of the branching set are known for dimension d ≤ 4. On the other hand, Izmestiev and Joswig described how ..."
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how to obtain a simplicial covering space (the partial unfolding) of a given simplicial complex, thus obtaining a simplicial branched cover [Adv. Geom. 3(2):191255, 2003]. We present a large class of branched covers which can be constructed via the partial unfolding. In particular, for d≤4 every
The Union of Balls and its Dual Shape
, 1993
"... Efficient algorithms are described for compuiing topological, combinatorial, and metric properties of ihe union of finitely many balls in R^d. These algorithms are based on a simplicial complex dual to a certain decomposition of the union of balls, and on short inclusionexclusion formulas derived f ..."
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Cited by 172 (12 self)
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Efficient algorithms are described for compuiing topological, combinatorial, and metric properties of ihe union of finitely many balls in R^d. These algorithms are based on a simplicial complex dual to a certain decomposition of the union of balls, and on short inclusionexclusion formulas derived
Constructible sheaves on simplicial complexes and Koszul
, 1998
"... Abstract. We obtain a linear algebra data presentation of the category Sh c (X,δ) of constructible with respect to perverse triangulation sheaves on a finite simplicial complex X. We also establish Koszul duality between Sh c (X, δ) and the category Mc(X, δ) of perverse sheaves constructible with re ..."
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Cited by 6 (3 self)
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Abstract. We obtain a linear algebra data presentation of the category Sh c (X,δ) of constructible with respect to perverse triangulation sheaves on a finite simplicial complex X. We also establish Koszul duality between Sh c (X, δ) and the category Mc(X, δ) of perverse sheaves constructible
Results 1  10
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912