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Your search keyword '"Homotopy operation"' showing total 4 results
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4 results on '"Homotopy operation"'

1. Toward Parallel Computation of Dense Homotopy Skeletons for nD Digital Objects

Author

Real, Pedro, Diaz-del-Rio, Fernando, Onchis, Darian, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Weikum, Gerhard, Series editor, Brimkov, Valentin E., editor, and Barneva, Reneta P., editor

Published
2017
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2. The realizability of operations on homotopy groups concentrated in two degrees.

Author

Baues, Hans-Joachim and Frankland, Martin

Subjects
*HOMOTOPY groups, *WHITEHEAD groups, *GROUP theory
Abstract

The homotopy groups of a space are endowed with homotopy operations which define the $$\varPi $$ -algebra of the space. An Eilenberg-MacLane space is the realization of a $$\varPi $$ -algebra concentrated in one degree. In this paper, we provide necessary and sufficient conditions for the realizability of a $$\varPi $$ -algebra concentrated in two degrees. We then specialize to the stable case, and list infinite families of such $$\varPi $$ -algebras that are not realizable. [ABSTRACT FROM AUTHOR]

Published
2015
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3. Toward Parallel Computation of Dense Homotopy Skeletons for nD Digital Objects

Author

Universidad de Sevilla. Departamento de Arquitectura y Tecnología de Computadores, Universidad de Sevilla. TEP-108: Robótica y Tecnología de Computadores Aplicada a la Rehabilitación, Ministerio de Economía y Competitividad (MINECO). España, Real Jurado, Pedro, Díaz del Río, Fernando, Onchis, Darian M., Universidad de Sevilla. Departamento de Arquitectura y Tecnología de Computadores, Universidad de Sevilla. TEP-108: Robótica y Tecnología de Computadores Aplicada a la Rehabilitación, Ministerio de Economía y Competitividad (MINECO). España, Real Jurado, Pedro, Díaz del Río, Fernando, and Onchis, Darian M.

Abstract

An appropriate generalization of the classical notion of abstract cell complex, called primal-dual abstract cell complex (pACC for short) is the combinatorial notion used here for modeling and analyzing the topology of nD digital objects and images. Let D ⊂ I be a set of n-xels (ROI) and I be a n-dimensional digital image.We design a theoretical parallel algorithm for constructing a topologically meaningful asymmetric pACC HSF(D), called Homological Spanning Forest of D (HSF of D, for short) starting from a canonical symmetric pACC associated to I and based on the application of elementary homotopy operations to activate the pACC processing units. From this HSF-graph representation of D, it is possible to derive complete homology and homotopy information of it. The preprocessing procedure of computing HSF(I) is thoroughly discussed. In this way, a significant advance in understanding how the efficient HSF framework for parallel topological computation of 2D digital images developed in [2] can be generalized to higher dimension is made.

Published
2017

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