Applications of perturbation theory to iterated fibrations

Lambe, Larry A.; Stasheff, Jim

doi:10.1007/bf01165893

Cited by 80 publications

(61 citation statements)

References 17 publications

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“…Finally f ∇ = 1. Without loss of generality (as demonstrated in [20]) one may assume in addition that the following relations (called the side conditions) hold:…”

Section: φ)mentioning

confidence: 99%

Transferring algebra structures up to homology equivalence

Johansson¹,

Lambe²

2001

MATH. SCAND.

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“…Finally f ∇ = 1. Without loss of generality (as demonstrated in [20]) one may assume in addition that the following relations (called the side conditions) hold:…”

Section: φ)mentioning

confidence: 99%

Transferring algebra structures up to homology equivalence

Johansson¹,

Lambe²

2001

MATH. SCAND.

Self Cite

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“…This notion is a special case of chain contraction [EL53] or strong deformation retraction data [LS87]. It is a usual tool for reducing chain complexes in order to compute their homology.…”

Section: Reductionmentioning

confidence: 99%

Cellular Skeletons: A New Approach to Topological Skeletons with Geometric Features

Gonzalez-Lorenzo

Bac²,

Mari³

et al. 2015

Computer Analysis of Images and Patterns

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Abstract. This paper introduces a new kind of skeleton for binary volumes called the cellular skeleton. This skeleton is not a subset of voxels of a volume nor a subcomplex of a cubical complex: it is a chain complex together with a reduction from the original complex.Starting from the binary volume we build a cubical complex which represents it regarding 6 or 26-connectivity. Then the complex is thinned using the proposed method based on elementary collapses, which preserves significant geometric features. The final step reduces the number of cells using Discrete Morse Theory. The resulting skeleton is a reduction which preserves the homology of the original complex and the geometrical information of the output of the previous step.The result of this method, besides its skeletonization content, can be used for computing the homology of the original complex, which usually provides well shaped homology generators.

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“…These three last are called side conditions [15]. In fact, these may always be assumed to hold, since the homotopy φ can be altered to satisfy these conditions [7,14].…”

Section: The Canonical Comparison Contraction a Necessary And Sufficmentioning

confidence: 99%

Comparison Maps for Relatively Free Resolutions

Álvarez

Armario

Frau

et al. 2006

Computer Algebra in Scientific Computing

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Abstract. Let Λ be a commutative ring, A an augmented differential graded algebra over Λ (briefly, DGA-algebra) and X be a relatively free resolution of Λ over A. The standard bar resolution of Λ over A, denoted by B(A), provides an example of a resolution of this kind. The comparison theorem gives inductive formulae f : B(A) → X and g: X → B(A) termed comparison maps. In case that f g = 1X and A is connected, we show that X is endowed a A∞-tensor product structure. In case that A is in addition commutative then (X, µX) is shown to be a commutative DGA-algebra with the product µX = f * (g ⊗ g) ( * is the shuffle product in B(A)). Furthermore, f and g are algebra maps. We give an example in order to illustrate the main results of this paper.

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Applications of perturbation theory to iterated fibrations

Cited by 80 publications

References 17 publications

Transferring algebra structures up to homology equivalence

Transferring algebra structures up to homology equivalence

Cellular Skeletons: A New Approach to Topological Skeletons with Geometric Features

Comparison Maps for Relatively Free Resolutions

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