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634
On rstacked triangulated manifolds
, 2013
"... The notion of rstackedness for simplicial polytopes was introduced by McMullen and Walkup in 1971 as a generalization of stacked polytopes. In this paper, we define the rstackedness for triangulated homology manifolds and study their basic properties. In addition, we find a new necessary conditi ..."
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Cited by 6 (1 self)
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The notion of rstackedness for simplicial polytopes was introduced by McMullen and Walkup in 1971 as a generalization of stacked polytopes. In this paper, we define the rstackedness for triangulated homology manifolds and study their basic properties. In addition, we find a new necessary
Computing Morse Functions on Triangulated Manifolds
 IN PROCEEDINGS OF THE SIAM SYMPOSIUM ON DISCRETE ALGORITHMS (SODA
, 1999
"... We describe an algorithm to compute a Morse function f on an abstract triangulated manifold of arbitrary dimension. We also describe an O(nff(n)) algorithm to compute the critical points of f and their Morse indices a 2manifold. This work has a variety of potential applications. ..."
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Cited by 7 (0 self)
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We describe an algorithm to compute a Morse function f on an abstract triangulated manifold of arbitrary dimension. We also describe an O(nff(n)) algorithm to compute the critical points of f and their Morse indices a 2manifold. This work has a variety of potential applications.
Auditory Morse Analysis of Triangulated Manifolds
 Mathematical Visualization
, 1998
"... Visualization of highdimensional or large geometric data sets is inherently difficult, so we experiment with the use of audio to display the shape and connectivity of these data sets. Sonification is used as both an addition to and a substitution for the visual display. We describe a new algorithm ..."
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Cited by 23 (0 self)
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Visualization of highdimensional or large geometric data sets is inherently difficult, so we experiment with the use of audio to display the shape and connectivity of these data sets. Sonification is used as both an addition to and a substitution for the visual display. We describe a new algorithm called wave traversal that provides a necessary intermediate step to sonification of the data; it produces an ordered sequence of subsets, called waves, that allows us to map the data to time. In this paper we focus in detail on the mathematics of wave traversal, in particular, how wave traversal can be used as a discrete Morse function.
Triangulated manifolds with few vertices: Combinatorial manifolds
, 2005
"... Let M be a simplicial manifold with n vertices. We call M centrally symmetric if it is invariant under an involution I of its vertex set which fixes no face of M. Obviously, the number of vertices of a centrally symmetric (triangulated) manifold is even, n = 2k, and, without loss of generality, we m ..."
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Cited by 19 (2 self)
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Let M be a simplicial manifold with n vertices. We call M centrally symmetric if it is invariant under an involution I of its vertex set which fixes no face of M. Obviously, the number of vertices of a centrally symmetric (triangulated) manifold is even, n = 2k, and, without loss of generality, we
WILSON FERMIONS ON A RANDOMLY TRIANGULATED MANIFOLD
, 1999
"... A general method of constructing the Dirac operator for a randomly triangulated manifold is proposed. The fermion field and the spin connection live, respectively, on the nodes and on the links of the corresponding dual graph. The construction is carried out explicitly in 2d, on an arbitrary orient ..."
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A general method of constructing the Dirac operator for a randomly triangulated manifold is proposed. The fermion field and the spin connection live, respectively, on the nodes and on the links of the corresponding dual graph. The construction is carried out explicitly in 2d, on an arbitrary
Triangulated Manifolds with Few Vertices: Geometric 3Manifolds
, 2003
"... The understanding and classification of (compact) 3dimensional manifolds (without boundary) is with no doubt one of the most prominent tasks in topology ever since Poincaré’s fundamental work [88] on ≪l’analysis situs≫ appeared in 1904. There are various ways for constructing 3manifolds, some of w ..."
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Cited by 12 (8 self)
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of which that are general enough to yield all 3manifolds (orientable or nonorientable) and some that produce only particular types or classes of examples. According to Moise [73], all 3manifolds can be triangulated. This implies that there are only countably many distinct combinatorial (and therefore
Triangulated Manifolds . . . : Centrally Symmetric Spheres and Products of Spheres
, 2004
"... Let M be a simplicial manifold with n vertices. We call M centrally symmetric if it is invariant under an involution I of its vertex set which fixes no face of M. Obviously, the number of vertices of a centrally symmetric (triangulated) manifold is even, n = 2k, and, without loss of generality, we m ..."
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Let M be a simplicial manifold with n vertices. We call M centrally symmetric if it is invariant under an involution I of its vertex set which fixes no face of M. Obviously, the number of vertices of a centrally symmetric (triangulated) manifold is even, n = 2k, and, without loss of generality, we
TOPOLOGICAL EMBEDDINGS OF TRIANGULATED MANIFOLDS IN A FOURDIMENSIONAI.A MANIFOLD
"... There is a long history to the study of locally flat and locally tame embeddings of manifolds. A few references would be [2], [3], [5]. Most previous results were either for embeddings into manifolds of dimension three or of dimension greater than four. Recent breakthroughs by l\1ichael Freedman hav ..."
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has previously studied topological embed mdings of triangulated manifolds M into a manifold Nn, n> 4, n m ~ 2, in which each open simplex of M is locally flat in N, and, in case n m < 3, each closed
Discrete DifferentialGeometry Operators for Triangulated 2Manifolds
, 2002
"... This paper provides a unified and consistent set of flexible tools to approximate important geometric attributes, including normal vectors and curvatures on arbitrary triangle meshes. We present a consistent derivation of these first and second order differential properties using averaging Vorono ..."
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Cited by 449 (14 self)
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This paper provides a unified and consistent set of flexible tools to approximate important geometric attributes, including normal vectors and curvatures on arbitrary triangle meshes. We present a consistent derivation of these first and second order differential properties using averaging Voronoi cells and the mixed FiniteElement/FiniteVolume method, and compare them to existing formulations. Building upon previous work in discrete geometry, these new operators are closely related to the continuous case, guaranteeing an appropriate extension from the continuous to the discrete setting: they respect most intrinsic properties of the continuous differential operators.
Results 1  10
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