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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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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
A discrete Morse theory for cell complexes
 in ‘‘Geometry, Topology 6 Physics for Raoul Bott
, 1995
"... In this paper we will present a very simple discrete Morse theory for CW complexes. In addition to proving analogues of the main theorems of Morse theory, we also present discrete analogues of such (seemingly) intrinsically smooth notions as the gradient vector field and the gradient ..."
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Cited by 233 (8 self)
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In this paper we will present a very simple discrete Morse theory for CW complexes. In addition to proving analogues of the main theorems of Morse theory, we also present discrete analogues of such (seemingly) intrinsically smooth notions as the gradient vector field and the gradient
Equivariant Discrete Morse Theory
, 2007
"... In this paper, we study Forman's discrete Morse theory in the case where a group acts on the underlying complex. We generalize the notion of a Morse matching, and obtain theory that can be used to simplify the description of the Ghomotopy type of a simplicial complex. As an application, we det ..."
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Cited by 3 (1 self)
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In this paper, we study Forman's discrete Morse theory in the case where a group acts on the underlying complex. We generalize the notion of a Morse matching, and obtain theory that can be used to simplify the description of the Ghomotopy type of a simplicial complex. As an application, we
Discrete Morse theory for Filtrations
, 2012
"... The central result of this dissertation is an extension of discrete Morse theory to filtered cell complexes. Discrete Morse theory imposes a pairing on some cells of a complex X and uses that pairing to introduce a new complex M – called the Morse complex – consisting of the unpaired cells of X alon ..."
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Cited by 1 (1 self)
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The central result of this dissertation is an extension of discrete Morse theory to filtered cell complexes. Discrete Morse theory imposes a pairing on some cells of a complex X and uses that pairing to introduce a new complex M – called the Morse complex – consisting of the unpaired cells of X
Discrete Morse Theory for Cellular Resolutions
 J. Reine Angew. Math
, 2000
"... We develop an analog of Forman's discrete Morse theory for cell complexes in the setting of cellular resolutions of multigraded monomial modules. In particular, using discrete Morse theory for cellular resolutions of multigraded ideals we are able to give minimal cellular resolutions for gen ..."
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Cited by 34 (2 self)
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We develop an analog of Forman's discrete Morse theory for cell complexes in the setting of cellular resolutions of multigraded monomial modules. In particular, using discrete Morse theory for cellular resolutions of multigraded ideals we are able to give minimal cellular resolutions
STATISTICAL PROPERTIES OF DYNAMICAL SYSTEMS WITH SOME HYPERBOLICITY
, 1997
"... This paper is about the ergodic theory of attractors and conservative dynamical systems with hyperbolic properties on large parts (though not necessarily all) of their phase spaces. The main results are for discrete time systems. To put this work into context, recall that for Axiom A attractors the ..."
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Cited by 260 (14 self)
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This paper is about the ergodic theory of attractors and conservative dynamical systems with hyperbolic properties on large parts (though not necessarily all) of their phase spaces. The main results are for discrete time systems. To put this work into context, recall that for Axiom A attractors
Constructing Discrete Morse Functions
, 2002
"... Morse theory has been considered a powerful tool in its applications to computational topology, computer graphics and geometric modeling. It was originally formulated for smooth manifolds. Recently, Robin Forman formulated a version of this theory for discrete structures such as cell complexes. It o ..."
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Cited by 8 (3 self)
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Morse theory has been considered a powerful tool in its applications to computational topology, computer graphics and geometric modeling. It was originally formulated for smooth manifolds. Recently, Robin Forman formulated a version of this theory for discrete structures such as cell complexes
Results 1  10
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