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QUANTIFYING HOMOLOGY CLASSES
, 2008
"... We develop a method for measuring homology classes. This involves three problems. First, we define the size of a homology class, using ideas from relative homology. Second, we define an optimal basis of a homology group to be the basis whose elements’ size have the minimal sum. We provide a greedy ..."
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Cited by 19 (3 self)
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We develop a method for measuring homology classes. This involves three problems. First, we define the size of a homology class, using ideas from relative homology. Second, we define an optimal basis of a homology group to be the basis whose elements’ size have the minimal sum. We provide a greedy
Measuring and localizing homology classes
 The Computing Research Repository (CoRR
, 2007
"... We develop a method for measuring and localizing homology classes. This involves two problems. First, we define relevant notions of size for both a homology class and a homology group basis, using ideas from relative homology. Second, we propose an algorithm to compute the optimal homology basis, us ..."
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Cited by 4 (0 self)
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We develop a method for measuring and localizing homology classes. This involves two problems. First, we define relevant notions of size for both a homology class and a homology group basis, using ideas from relative homology. Second, we propose an algorithm to compute the optimal homology basis
Moving Homology Classes to Infinity
 Forum Math
"... Abstract. Let q: ˜ X → X be a regular covering over a finite polyhedron with free abelian group of covering translations. Each nonzero cohomology class ξ ∈ H 1 (X; R) with q ∗ ξ = 0 determines a notion of “infinity ” of the noncompact space ˜ X. In this paper we characterize homology classes z in ˜ ..."
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Cited by 6 (4 self)
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Abstract. Let q: ˜ X → X be a regular covering over a finite polyhedron with free abelian group of covering translations. Each nonzero cohomology class ξ ∈ H 1 (X; R) with q ∗ ξ = 0 determines a notion of “infinity ” of the noncompact space ˜ X. In this paper we characterize homology classes z
ON HOMOLOGY CLASSES NOT REPRESENTABLE BY PRODUCTS
, 804
"... ABSTRACT. We show that Preissmann’s theorem implies that no closed negatively curved manifold is dominated by a nontrivial product. We also show that a fiber bundle whose base and fiber are negatively curved is dominated by a product if and only if it has a finite covering space which is a trivial ..."
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ABSTRACT. We show that Preissmann’s theorem implies that no closed negatively curved manifold is dominated by a nontrivial product. We also show that a fiber bundle whose base and fiber are negatively curved is dominated by a product if and only if it has a finite covering space which is a trivial bundle. 1.
CHEBOTAREVTYPE THEOREMS IN HOMOLOGY CLASSES
"... Abstract. We describe how closed geodesics lying in a prescribed homology class on a negatively curved manifold split when lifted to a finite cover. This generalizes a result of Zelditch in the case of compact hyperbolic surfaces. Given a compact manifold of negative curvature, there are geometric a ..."
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Abstract. We describe how closed geodesics lying in a prescribed homology class on a negatively curved manifold split when lifted to a finite cover. This generalizes a result of Zelditch in the case of compact hyperbolic surfaces. Given a compact manifold of negative curvature, there are geometric
Representing homology classes by locally flat surfaces of minimum genus
 Amer. J. Math
, 1997
"... homology classes by locally flat surfaces of minimum genus ..."
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Cited by 4 (0 self)
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homology classes by locally flat surfaces of minimum genus
Symplectic surfaces in a fixed homology class
 J. Differential Geom
, 1999
"... The purpose of this paper is to investigate the following problem: For a fixed 2dimensional homology class α in a simply connected symplectic 4manifold, up to smooth isotopy, how many connected smoothly embedded symplectic submanifolds represent α? ..."
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Cited by 37 (6 self)
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The purpose of this paper is to investigate the following problem: For a fixed 2dimensional homology class α in a simply connected symplectic 4manifold, up to smooth isotopy, how many connected smoothly embedded symplectic submanifolds represent α?
Nonisotopic symplectic tori in the same homology class
"... Abstract. For any pair of integers n≥1 and q ≥ 2, we construct an infinite family of mutually nonisotopic symplectic tori representing the homology class q[F] of an elliptic surface E(n), where [F] is the homology class of the fiber. We also show how such families can be nonisotopically and symple ..."
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Cited by 12 (4 self)
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Abstract. For any pair of integers n≥1 and q ≥ 2, we construct an infinite family of mutually nonisotopic symplectic tori representing the homology class q[F] of an elliptic surface E(n), where [F] is the homology class of the fiber. We also show how such families can be non
Asymptotic expansion for cycles in homology classes for graphs
, 2004
"... Abstract. In this paper we give an asymptotic expansion including error terms for the number of cycles in homology classes for connected graphs. Mainly, we obtain formulae about the coefficients of error terms which depend on the homology classes and give two examples of how to calculate the coeffic ..."
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Abstract. In this paper we give an asymptotic expansion including error terms for the number of cycles in homology classes for connected graphs. Mainly, we obtain formulae about the coefficients of error terms which depend on the homology classes and give two examples of how to calculate
Results 1  10
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162,241