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SIMPLICIAL EMBEDDINGS BETWEEN PANTS GRAPHS
, 2009
"... We prove that, except in some lowcomplexity cases, every locally injective simplicial map between pants graphs is induced by a π1injective embedding between the corresponding surfaces. ..."
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Cited by 3 (2 self)
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We prove that, except in some lowcomplexity cases, every locally injective simplicial map between pants graphs is induced by a π1injective embedding between the corresponding surfaces.
SIMPLICIAL ENERGY AND SIMPLICIAL HARMONIC MAPS
"... Abstract. We introduce a combinatorial energy for maps of triangulated surfaces with simplicial metrics and analyze the existence and uniqueness properties of the corresponding harmonic maps. We show that some important applications of smooth harmonic maps can be obtained in this setting. 1. ..."
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Abstract. We introduce a combinatorial energy for maps of triangulated surfaces with simplicial metrics and analyze the existence and uniqueness properties of the corresponding harmonic maps. We show that some important applications of smooth harmonic maps can be obtained in this setting. 1.
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
On 3Simplicial Vertices in Planar Graphs
, 2001
"... A vertex v in a graph G = (V, E) is ksimplicial if the neighborhood N(v) of v can be vertexcovered by k or fewer complete graphs. The main result of the paper states that a planar graph of order at least four has at least four 3simplicial vertices of degree at most five. This result is a stren ..."
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A vertex v in a graph G = (V, E) is ksimplicial if the neighborhood N(v) of v can be vertexcovered by k or fewer complete graphs. The main result of the paper states that a planar graph of order at least four has at least four 3simplicial vertices of degree at most five. This result is a
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
Simplicial moves on complexes and manifolds
 GEOMETRY & TOPOLOGY MONOGRAPHS VOLUME 2: PROCEEDINGS OF THE KIRBYFEST PAGES 299–320
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Simplicial Quantum Gravity
, 1997
"... We analyze two models of random geometries: planar hypercubic random surfaces and four dimensional simplicial quantum gravity. We show for the hypercubic random surface model that a geometrical constraint does not change the critical properties of the model compared to the model without this const ..."
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Cited by 1 (0 self)
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We analyze two models of random geometries: planar hypercubic random surfaces and four dimensional simplicial quantum gravity. We show for the hypercubic random surface model that a geometrical constraint does not change the critical properties of the model compared to the model without
Simplicial and Singular Homology
"... > Z p (K), and we define the homology group H p (K) as the quotient group H p (K) = Z p (K)=B p (K): What makes the homology groups of a complex interesting, is that they only depend on the geometric realization K g of the complex K, and not on the various complexes representing K g . Proving t ..."
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this fact requires relatively hard work, and we refer the reader to Munkres [9] or Rotman [10], for a proof. The first step in defining simplicial homology groups is to define oriented simplices. Given a complex K = (K (0) ; K), recall that an nsimplex is a subset oe = fff 0 ; : : : ; ff n g o
Saturated Simplicial Complexes
, 2004
"... Among shellable complexes a certain class has maximal modular homology, and these are the socalled saturated complexes. We extend the notion of saturation to arbitrary pure complexes and give a survey of their properties. It is shown that saturated complexes can be characterized via the prank of i ..."
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Among shellable complexes a certain class has maximal modular homology, and these are the socalled saturated complexes. We extend the notion of saturation to arbitrary pure complexes and give a survey of their properties. It is shown that saturated complexes can be characterized via the prank of incidence matrices and via the structure of links. We show that rankselected subcomplexes of saturated complexes are also saturated, and that order complexes of geometric lattices are saturated.
Results 1  10
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61,110