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The cube axiom and resolutions in homotopy theory
We show that a version of the cube axiom holds in cosimplicial unstable coalgebras and cosimplicial spaces equipped with a resolution model...
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Eilenberg–Maclane spaces and stabilisation in homotopy type theory
In this note, we study the deloo** of spaces and maps in homotopy type theory. We show that in some cases, spaces have a unique deloo**, and give...
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Random simple-homotopy theory
We implement an algorithm RSHT (random simple-homotopy) to study the simple-homotopy types of simplicial complexes, with a particular focus on...
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Homotopy Theory: Fundamental Group and Higher Homotopy Groups
This chapter officially inaugurates homotopy theory to begin a study of algebraic topology by conveying the basic concepts of homotopy and...
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Homotopy prefactorization algebras
We apply the theory of operadic Koszul duality to provide a cofibrant resolution of the colored operad whose algebras are prefactorization algebras...
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Weak Graph Map Homotopy and Its Applications
The authors introduce a notion of a weak graph map homotopy (they call it M -homotopy), discuss its properties and applications. They prove that the...
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Weight Decompositions on Algebraic Models for Map** Spaces and Homotopy Automorphisms
We obtain restrictions on the rational homotopy types of map** spaces and of classifying spaces of homotopy automorphisms by means of the theory of...
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A homotopy analysis solution to large deformation of a nanowire based on nonlocal elasticity theory
On the basis of Eringen’s nonlocal elasticity theory, large deflection of a cantilever nanowire under a uniformly distributed load is investigated...
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Homotopy Theory in Digital Topology
Digital topology is part of the ongoing endeavor to understand and analyze digitized images. With a view to supporting this endeavor, many notions...
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The Homotopy Type of G/TOP, G/PL and G/O
In this chapter we review how to determine the homotopy types of the spaces G/PL and G/TOP and discuss some related results. We have already seen the...
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Homotopy Sheaves on Generalised Spaces
We study the homotopy right Kan extension of homotopy sheaves on a category to its free cocompletion, i.e. to its category of presheaves. Any...
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From samples to persistent stratified homotopy types
The natural occurrence of singular spaces in applications has led to recent investigations on performing topological data analysis (TDA) in a...
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Homotopy commutativity in symmetric spaces
We extend previous results of Ganea and the two of the authors with Takeda on the homotopy commutativity of the loop spaces of Hermitian symmetric...
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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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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...