scholarly journals Coronas for properly combable spaces

2021 ◽  
pp. 1-83
Author(s):  
Alexander Engel ◽  
Christopher Wulff
Keyword(s):  
Compact Space ◽  
Systematic Approach ◽  
Cohomological Dimension ◽  
Text Structure ◽  
Asymptotic Dimension ◽  
Finite Model ◽  
Classifying Space ◽  
Rips Complex ◽  
Complex Construction ◽  
Assembly Map

This paper is a systematic approach to the construction of coronas (i.e. Higson dominated boundaries at infinity) of combable spaces. We introduce three additional properties for combings: properness, coherence and expandingness. Properness is the condition under which our construction of the corona works. Under the assumption of coherence and expandingness, attaching our corona to a Rips complex construction yields a contractible [Formula: see text]-compact space in which the corona sits as a [Formula: see text]-set. This results in bijectivity of transgression maps, injectivity of the coarse assembly map and surjectivity of the coarse co-assembly map. For groups we get an estimate on the cohomological dimension of the corona in terms of the asymptotic dimension. Furthermore, if the group admits a finite model for its classifying space [Formula: see text], then our constructions yield a [Formula: see text]-structure for the group.

Evaluation of Delay Factors in Jacket Structure Project

2016 ◽  
Vol 836 ◽  
pp. 317-322
Author(s):  
Silvianita ◽  
Andika Trisna Putra ◽  
Daniel M. Rosyid ◽  
Dirta Marina Chamelia ◽  
Imam Rochani
Keyword(s):  
Systematic Approach ◽  
Fault Tree Analysis ◽  
Analysis Data ◽  
Offshore Platforms ◽  
Construction Process ◽  
Time Schedule ◽  
Assembly Structure ◽  
Complex Construction ◽  
Main Factors ◽  
Design Construction

Offshore platforms are used worldwide for drrilling, proceesing and even storage purposes. The offshore platforms can be fixed to the seabed, or can be float. The fixed platform namely jacket structure is a complex construction and design. Construction process of the jacket structure sometimes is not in accordance with the time schedule. There are many factors affect them, limited time, equipment, materials required, and cost of human resources. In order to analyze the delay factors of a jacket project requires a systematic approach. This paper will discusses the delay factors of the construction of Jacket Structure using FTA (Fault Tree Analysis). Data is obtained from one fabrication company which involve their experts to identify the contribution of delay project. There are three main factors causing the Jacket project delay namely Long Process of Procurement, Late Schecule of Assembly Structure, and Bad Management.

Bounded rigidity of manifolds and asymptotic dimension growth

2008 ◽  
Vol 1 (1) ◽  
pp. 129-144 ◽  
Author(s):  
Stanley S. Chang ◽  
Steven Ferry ◽  
Guoliang Yu
Keyword(s):  
Asymptotic Dimension ◽  
Rigidity Result ◽  
Asymptotic Growth ◽  
Bounded Geometry ◽  
Definition Of ◽  
Assembly Map

AbstractWe provide a bounded rigidity result for uniformly contractible manifolds with bounded geometry and sufficiently slow asymptotic dimension growth. This notion of asymptotic growth is a generalization of Gromov's definition of asymptotic dimension. In particular for these manifolds we prove that the bounded assembly map is an isomorphism. Our result is inspired by the coarse Baum-Connes results of Yu and the development of squeezing structures.

scholarly journals On modules over infinite group rings

2016 ◽  
Vol 26 (03) ◽  
pp. 451-466 ◽  
Author(s):  
Gunnar Carlsson ◽  
Boris Goldfarb
Keyword(s):  
Group Ring ◽  
Discrete Group ◽  
Infinite Group ◽  
Homological Dimension ◽  
Group Rings ◽  
Finite Model ◽  
Classifying Space ◽  
Projective Resolutions ◽  
Algebraic Formula ◽  
Important Object

Let [Formula: see text] be a commutative ring and [Formula: see text] be an infinite discrete group. The algebraic [Formula: see text]-theory of the group ring [Formula: see text] is an important object of computation in geometric topology and number theory. When the group ring is Noetherian, there is a companion [Formula: see text]-theory of [Formula: see text] which is often easier to compute. However, it is exceptionally rare that the group ring is Noetherian for an infinite group. In this paper, we define a version of [Formula: see text]-theory for any finitely generated discrete group. This construction is based on the coarse geometry of the group. It has some expected properties such as independence from the choice of a word metric. We prove that, whenever [Formula: see text] is a regular Noetherian ring of finite global homological dimension and [Formula: see text] has finite asymptotic dimension and a finite model for the classifying space [Formula: see text], the natural Cartan map from the [Formula: see text]-theory of [Formula: see text] to [Formula: see text]-theory is an equivalence. On the other hand, our [Formula: see text]-theory is indeed better suited for computation as we show in a separate paper. Some results and constructions in this paper might be of independent interest as we learn to construct projective resolutions of finite type for certain modules over group rings.

scholarly journals Topological 4-manifolds with right-angled Artin fundamental groups

2019 ◽  
Vol 11 (04) ◽  
pp. 777-821
Author(s):  
Ian Hambleton ◽  
Alyson Hildum
Keyword(s):  
Fundamental Group ◽  
Cohomological Dimension ◽  
Fundamental Groups ◽  
Connected Sum ◽  
Dimension Formula ◽  
Assembly Map ◽  
Torsion Free

We classify closed, spin[Formula: see text], topological [Formula: see text]-manifolds with fundamental group [Formula: see text] of cohomological dimension [Formula: see text] (up to [Formula: see text]-cobordism), after stabilization by connected sum with at most [Formula: see text] copies of [Formula: see text]. In general, we must also assume that [Formula: see text] satisfies certain [Formula: see text]-theory and assembly map conditions. Examples for which these conditions hold include the torsion-free fundamental groups of [Formula: see text]-manifolds and all right-angled Artin groupswhose defining graphs have no [Formula: see text]-cliques.

A homotopy decomposition for the classifying space of virtually torsion-free groups and applications

1996 ◽  
Vol 120 (4) ◽  
pp. 663-686 ◽  
Author(s):  
Chun-Nip Lee
Keyword(s):  
Automorphism Groups ◽  
Free Groups ◽  
Outer Automorphism ◽  
Cohomological Dimension ◽  
Finite Graph ◽  
Mapping Class ◽  
Classifying Space ◽  
Homotopy Decomposition ◽  
Torsion Free Subgroup ◽  
Torsion Free

Let Γ be a discrete group. Γ is said to have finite virtual cohomological dimension (vcd) if there exists a finite index torsion-free subgroup Γ' of Γ such that Γ' has finite cohomological dimension over . Examples of such groups include the fundamental group of a finite graph of finite groups, arithmetic groups, mapping class groups and outer automorphism groups of free groups. One of the fundamental problems in topology is to understand the cohomology of these finite vcd-groups.

Random models and solvable Skolem classes

1993 ◽  
Vol 58 (3) ◽  
pp. 908-914
Author(s):  
Warren Goldfarb
Keyword(s):  
Normal Form ◽  
Systematic Approach ◽  
Finite Model ◽  
Theoretic Property ◽  
Quantification Theory ◽  
Maslov Class ◽  
Random Models ◽  
Universal Quantifiers ◽  
Necessary And Sufficient ◽  
Made In

A Skolem class is a class of formulas of pure quantification theory in Skolem normal form: closed, prenex formulas with prefixes ∀…∀∃…∃. (Pure quantification theory contains quantifiers, truth-functions, and predicate letters, but neither the identity sign nor function letters.) The Gödel Class, in which the number of universal quantifiers is limited to two, was shown effectively solvable (for satisfiability) sixty years ago [G1]. Various solvable Skolem classes that extend the Gödel Class can be obtained by allowing more universal quantifiers but restricting the combinations of variables that may occur together in atomic subformulas [DG, Chapter 2]. The Gödel Class and these extensions are also finitely controllable, that is, every satisfiable formula in them has a finite model. In this paper we isolate a model-theoretic property that connects the usual solvability proofs for these classes and their finite controllability. For formulas in the solvable Skolem classes, the property is necessary and sufficient for satisfiability. The solvability proofs implicitly relied on this fact. Moreover, for any formula in Skolem normal form, the property implies the existence of a finite model.The proof of the latter implication uses the random models technique introduced in [GS] for the Gödel Class and modified and applied in [Go] to the Maslov Class. The proof thus substantiates the claim made in [Go] that random models can be adapted to the Skolem classes of [DG, Chapter 2]. As a whole, the results of this paper provide a more general, systematic approach to finite controllability than previous methods.

Reading Longer Words: Insights Into Multisyllabic Word Reading

2017 ◽  
Vol 2 (1) ◽  
pp. 86-94 ◽  
Author(s):  
Lindsay Heggie ◽  
Lesly Wade-Woolley
Keyword(s):  
Systematic Approach ◽  
Word Reading ◽  
Explicit Instruction ◽  
Working Memory Capacity ◽  
Reading Difficulties ◽  
Instructional Programs ◽  
Morphological Knowledge ◽  
Morphological Complexity ◽  
Reading Accuracy ◽  
Grade 3

Students with persistent reading difficulties are often especially challenged by multisyllabic words; they tend to have neither a systematic approach for reading these words nor the confidence to persevere (Archer, Gleason, & Vachon, 2003; Carlisle & Katz, 2006; Moats, 1998). This challenge is magnified by the fact that the vast majority of English words are multisyllabic and constitute an increasingly large proportion of the words in elementary school texts beginning as early as grade 3 (Hiebert, Martin, & Menon, 2005; Kerns et al., 2016). Multisyllabic words are more difficult to read simply because they are long, posing challenges for working memory capacity. In addition, syllable boundaries, word stress, vowel pronunciation ambiguities, less predictable grapheme-phoneme correspondences, and morphological complexity all contribute to long words' difficulty. Research suggests that explicit instruction in both syllabification and morphological knowledge improve poor readers' multisyllabic word reading accuracy; several examples of instructional programs involving one or both of these elements are provided.

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