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1,123
A combinatorial description of knot Floer homology
, 2006
"... Given a grid presentation of a knot (or link) K in the threesphere, we describe a Heegaard diagram for the knot complement in which the Heegaard surface is a torus and all elementary domains are squares. Using this diagram, we obtain a purely combinatorial description of the knot Floer homology of ..."
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Cited by 109 (30 self)
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Given a grid presentation of a knot (or link) K in the threesphere, we describe a Heegaard diagram for the knot complement in which the Heegaard surface is a torus and all elementary domains are squares. Using this diagram, we obtain a purely combinatorial description of the knot Floer homology
A combinatorial description of monomial algebras
, 2009
"... This paper is concerned with the combinatorial description of the graded minimal free resolution of certain monomial algebras which includes toric rings. Concretely, we explicitly describe how the graded minimal free resolution of those algebras is related to the combinatorics of some simplicial com ..."
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This paper is concerned with the combinatorial description of the graded minimal free resolution of certain monomial algebras which includes toric rings. Concretely, we explicitly describe how the graded minimal free resolution of those algebras is related to the combinatorics of some simplicial
Combinatorial descriptions of toric extremal contractions
 Nagoya Math. J
"... Abstract. In this paper, we give explicit combinatorial descriptions for toric extremal contractions under the relative setting, where varieties do not need to be complete. Fujino’s completion theorem is the key to the main result. As applications, we can generalize some of Mustat¸ǎ’s results relate ..."
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Cited by 3 (1 self)
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Abstract. In this paper, we give explicit combinatorial descriptions for toric extremal contractions under the relative setting, where varieties do not need to be complete. Fujino’s completion theorem is the key to the main result. As applications, we can generalize some of Mustat¸ǎ’s results
Combinatorial descriptions of the homotopy groups of certain spaces
 Math. Proc. Camb. Philos. Soc
"... Abstract. We give a combinatorial description of homotopy groups of ΣK(π, 1). In particular, all of the homotopy groups of the 3sphere are combinatorially given. 1. ..."
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Cited by 33 (24 self)
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Abstract. We give a combinatorial description of homotopy groups of ΣK(π, 1). In particular, all of the homotopy groups of the 3sphere are combinatorially given. 1.
COMBINATORIAL DESCRIPTION OF THE HOMOTOPY GROUPS OF WEDGE OF SPHERES
"... Abstract. In this paper, we give a combinatorial description of the homotopy groups of a wedge of spheres. This result generalizes that of J. Wu on the homotopy groups of a wedge of 2spheres. In particular, the higher homotopy groups of spheres are given as the centers of certain combinatorially de ..."
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Cited by 2 (0 self)
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Abstract. In this paper, we give a combinatorial description of the homotopy groups of a wedge of spheres. This result generalizes that of J. Wu on the homotopy groups of a wedge of 2spheres. In particular, the higher homotopy groups of spheres are given as the centers of certain combinatorially
A combinatorial description of knotted surfaces and their isotopies
 MR MR1445361 (98c:57023
, 1997
"... We discuss the diagrammatic theory of knot isotopies in dimension 4. We project a knotted surface to a threedimensional space and arrange the surface to have generic singularities upon further projection to a plane. We examine the singularities in this plane as an isotopy is performed, and give a ..."
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Cited by 34 (8 self)
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finite set of local moves to the singular set that can be used to connect any two isotopic knottings. We show how the notion of projections of isotopies can be used to give a combinatoric description of knotted surfaces that is sufficient for categorical applications. In this description, knotted
Combinatorial description of the roots of the BernsteinSato polynomials for monomial ideals
, 2005
"... We give a combinatorial description of the roots of the BernsteinSato polynomial of a monomial ideal using the Newton polyhedron and some semigroups associated to the ideal. ..."
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Cited by 8 (6 self)
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We give a combinatorial description of the roots of the BernsteinSato polynomial of a monomial ideal using the Newton polyhedron and some semigroups associated to the ideal.
A combinatorial description of some Heegaard Floer homologies
"... Abstract. In this paper, we give an algorithm to compute the hat version of the Heegaard Floer homology of a 3manifold. This method also allows us to compute the filtrations coming from a knot in a 3manifold. 1. ..."
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Cited by 25 (4 self)
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Abstract. In this paper, we give an algorithm to compute the hat version of the Heegaard Floer homology of a 3manifold. This method also allows us to compute the filtrations coming from a knot in a 3manifold. 1.
A COMBINATORIAL DESCRIPTION OF THE HEEGAARD FLOER CONTACT INVARIANT
, 2006
"... Abstract. In this short note, we observe that the Heegaard Floer contact invariant is combinatorial by applying the algorithm of Sarkar–Wang to the description of the contact invariant due to Honda–Kazez–Matić. We include an example of this combinatorial calculation. 1. ..."
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Cited by 11 (0 self)
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Abstract. In this short note, we observe that the Heegaard Floer contact invariant is combinatorial by applying the algorithm of Sarkar–Wang to the description of the contact invariant due to Honda–Kazez–Matić. We include an example of this combinatorial calculation. 1.
COMBINATORIAL DESCRIPTIONS OF MULTIVERTEX 2COMPLEXES
, 909
"... Abstract. Group presentations are implicit descriptions of 2dimensional cell complexes with only one vertex. While such complexes are usually sufficient for topological investigations of groups, multivertex complexes are often preferable when the focus shifts to geometric considerations. In this a ..."
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Abstract. Group presentations are implicit descriptions of 2dimensional cell complexes with only one vertex. While such complexes are usually sufficient for topological investigations of groups, multivertex complexes are often preferable when the focus shifts to geometric considerations
Results 1  10
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1,123