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Homotopy, homology, and persistent homology using closure spaces
We develop persistent homology in the setting of filtrations of (Čech) closure spaces. Examples of filtrations of closure spaces include metric...
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Topology of Fiber Bundles: Homotopy Theory of Bundles
This chapter continues the study topology of fiber bundles, which has created general interest as it involves interesting applications of topology to...
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K-flatness and orthogonality in homotopy categories
K-flatness for unbounded complexes of modules over a ring R was introduced by Spaltenstein [27], as an analogue of the classical notion of flatness...
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Simplicial and Dendroidal Homotopy Theory
This open access book offers a self-contained introduction to the homotopy theory of simplicial and dendroidal sets and spaces. These are essential...
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Homotopy
Retracts, deformation retracts, homotopy of maps and paths are all discussed here. All the material needed to define fundamental groups in the next...
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A new type of fixed point theorem via interpolation of operators with application in homotopy theory
The purpose of this paper is to introduce the class of multi-valued operators by the technique of interpolation of operators. Our results extend and...
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2-local unstable homotopy groups of indecomposable A
3 2 -complexesIn this paper, we calculate the 2-local unstable homotopy groups of indecomposable A
3 2 -complexes. The main technique used is analysing the homotopy... -
Homotopy
There’s an intuitive notion of ‘equivalence of shapes’ in topology that is broader than the concept of homeomorphism. Two connected regular subsets...
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Combined Homotopy and Galerkin Stability Analysis of Mathieu-Like Equations
We propose a homotopy analysis method in combination with Galerkin projections to obtain transition curves of Mathieu-like equations. While...
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A spline smoothing homotopy method for nonlinear programming problems with both inequality and equality constraints
In this paper, we construct a new spline smoothing homotopy method for solving general nonlinear programming problems with a large number of...
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Analytic Detection in Homotopy Groups of Smooth Manifolds
In this paper, for the map** of a sphere into a compact orientable manifold S n → M , n ≥ 1, we solve the problem of determining whether it...
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On Localized Self-Homotopy Groups of SU(4) and Sp(4)
In this article, first, localizing at odd primes p , we study the self-homotopy groups of SU (4) and Sp (4). Second, we consider the homotopy nilpotency...
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Classifying Leavitt path algebras up to involution preserving homotopy
We prove that the Bowen–Franks group classifies the Leavitt path algebras of purely infinite simple finite graphs over a regular supercoherent...
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An Optimal Homotopy Analysis Transform Method for Handling Nonlinear PDEs
In this paper, we present an optimal homotopy analysis transform method to deal with nonlinear PDEs. The suggested method constructs an optimal...
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A Polyhedral Homotopy Algorithm for Real Zeros
We design a homotopy continuation algorithm, that is based on Viro’s patchworking method, for finding real zeros of sparse polynomial systems. The...
