scholarly journals On the classification of Smale–Barden manifolds with Sasakian structures

2021 ◽  
pp. 2150077
Author(s):  
Vicente Muñoz ◽  
Aleksy Tralle
Keyword(s):  
Complete Solution ◽  
Rational Homology ◽  
Sasakian Structure ◽  
Difficult Question ◽  
Rational Homology Spheres ◽  
Sasakian Structures ◽  
Simply Connected

Smale–Barden manifolds [Formula: see text] are classified by their second homology [Formula: see text] and the Barden invariant [Formula: see text]. It is an important and difficult question to decide when [Formula: see text] admits a Sasakian structure in terms of these data. In this work, we show methods of doing this. In particular, we realize all [Formula: see text] with [Formula: see text] and [Formula: see text] provided that [Formula: see text], [Formula: see text], [Formula: see text] are pairwise coprime. We give a complete solution to the problem of the existence of Sasakian structures on rational homology spheres in the class of semi-regular Sasakian structures. Our method allows us to completely solve the following problem of Boyer and Galicki in the class of semi-regular Sasakian structures: determine which simply connected rational homology 5-spheres admit negative Sasakian structures.

scholarly journals ON ALEXANDER MODULES AND BLANCHFIELD FORMS OF NULL-HOMOLOGOUS KNOTS IN RATIONAL HOMOLOGY SPHERES

2012 ◽  
Vol 21 (05) ◽  
pp. 1250042 ◽  
Author(s):  
DELPHINE MOUSSARD
Keyword(s):  
Isomorphism Class ◽  
The Other ◽  
Rational Homology ◽  
Rational Homology Spheres

In this paper, we give a classification of Alexander modules of null-homologous knots in rational homology spheres. We characterize these modules [Formula: see text] equipped with their Blanchfield forms ϕ, and the modules [Formula: see text] such that there is a unique isomorphism class of [Formula: see text], and we prove that for the other modules [Formula: see text], there are infinitely many such classes. We realize all these [Formula: see text] by explicit knots in ℚ-spheres.

scholarly journals Brieskorn manifolds, positive Sasakian geometry, and contact topology

2016 ◽  
Vol 28 (5) ◽  
pp. 943-965
Author(s):  
Charles P. Boyer ◽  
Leonardo Macarini ◽  
Otto van Koert
Keyword(s):  
Moduli Space ◽  
Einstein Metrics ◽  
Contact Structures ◽  
Rational Homology ◽  
Contact Topology ◽  
Connected Sums ◽  
New Family ◽  
Rational Homology Spheres ◽  
Sasakian Geometry ◽  
Sasakian Structures

AbstractUsing ${S^{1}}$-equivariant symplectic homology, in particular its mean Euler characteristic, of the natural filling of links of Brieskorn–Pham polynomials, we prove the existence of infinitely many inequivalent contact structures on various manifolds, including in dimension 5 the k-fold connected sums of ${S^{2}\times S^{3}}$ and certain rational homology spheres. We then apply our result to show that on these manifolds the moduli space of classes of positive Sasakian structures has infinitely many components. We also apply our results to give lower bounds on the number of components of the moduli space of Sasaki–Einstein metrics on certain homotopy spheres. Finally, a new family of Sasaki–Einstein metrics of real dimension 20 on ${S^{5}}$ is exhibited.

scholarly journals Geometric and Topological Bases of a New Classification of Wood Vascular Tissues Part 1: Shape and Arrangement Classifications of Vessels

2021 ◽  
Vol 13 (14) ◽  
pp. 7545
Author(s):  
Nikolai Bardarov ◽  
Vladislav Todorov ◽  
Nicole Christoff
Keyword(s):  
Computer Vision ◽  
Detailed Analysis ◽  
Tree Species ◽  
Complete Solution ◽  
New Classification ◽  
Topological Characteristics ◽  
Definition Of ◽  
Wood Science ◽  
Quantitative Indicators

The need to identify wood by its anatomical features requires a detailed analysis of all the elements that make it up. This is a significant problem of structural wood science, the most general and complete solution of which is yet to be sought. In recent years, increasing attention has been paid to the use of computer vision methods to automate processes such as the detection, identification, and classification of different tissues and different tree species. The more successful use of these methods in wood anatomy requires a more precise and comprehensive definition of the anatomical elements, according to their geometric and topological characteristics. In this article, we conduct a detailed analysis of the limits of variation of the location and grouping of vessels in the observed microscopic samples. The present development offers criteria and quantitative indicators for defining the terms shape, location, and group of wood tissues. It is proposed to differentiate the quantitative indicators of the vessels depending on their geometric and topological characteristics. Thus, with the help of computer vision technics, it will be possible to establish topological characteristics of wood vessels, the extraction of which would be used to develop an algorithm for the automatic classification of tree species.

scholarly journals The even Clifford structure of the fourth Severi variety

2015 ◽  
Vol 2 (1) ◽  
Author(s):  
Maurizio Parton ◽  
Paolo Piccinni
Keyword(s):  
Vector Bundle ◽  
Riemannian Manifolds ◽  
Severi Variety ◽  
Simply Connected

AbstractTheHermitian symmetric spaceM = EIII appears in the classification of complete simply connected Riemannian manifolds carrying a parallel even Clifford structure [19]. This means the existence of a real oriented Euclidean vector bundle E over it together with an algebra bundle morphism φ : Cl

Strongly-cyclic branched coverings and the Alexander polynomial of knots in rational homology spheres

2007 ◽  
Vol 142 (2) ◽  
pp. 259-268 ◽  
Author(s):  
YUYA KODA
Keyword(s):  
Fundamental Group ◽  
Homology Group ◽  
Alexander Polynomial ◽  
Homology Sphere ◽  
Cyclic Covering ◽  
Rational Homology ◽  
Branched Coverings ◽  
Branched Covering ◽  
Rational Homology Spheres ◽  
Rational Homology Sphere

AbstractLet K be a knot in a rational homology sphere M. In this paper we correlate the Alexander polynomial of K with a g-word cyclic presentation for the fundamental group of the strongly-cyclic covering of M branched over K. We also give a formula for the order of the first homology group of the strongly-cyclic branched covering.

In-Line Sorting of Processed Fruit Using Computer Vision

2013 ◽  
pp. 874-895
Author(s):  
J. Blasco ◽  
N. Aleixos ◽  
S. Cubero ◽  
F. Albert ◽  
D. Lorente ◽  
...  
Keyword(s):  
Machine Vision ◽  
Fruits And Vegetables ◽  
Complete Solution ◽  
Punica Granatum ◽  
Automatic Inspection ◽  
Minimally Processed ◽  
Total Absence ◽  
Similar Appearance ◽  
Punica Granatum L

Nowadays, there is a growing demand for quality fruits and vegetables that are simple to prepare and consume, like minimally processed fruits. These products have to accomplish some particular characteristics to make them more attractive to the consumers, like a similar appearance and the total absence of external defects. Although recent advances in machine vision have allowed for the automatic inspection of fresh fruit and vegetables, there are no commercially available equipments for sorting of minority processed fruits, like arils of pomegranate (Punica granatum L) or segments of Satsuma mandarin (Citrus unshiu) ready to eat. This work describes a complete solution based on machine vision for the automatic inspection and classification of these fruits based on their estimated quality. The classification is based on morphological and colour features estimated from images taken in-line, and their analysis using statistical methods in order to grade the fruit into commercial categories.

Surgery Theory and the Classification of Closed, Simply Connected 4-manifolds

2021 ◽  
pp. 331-352
Author(s):  
Patrick Orson ◽  
Mark Powell ◽  
Arunima Ray
Keyword(s):  
Embedding Theorem ◽  
Surgery Theory ◽  
Simply Connected

Surgery theory and the classification of simply connected 4-manifolds comprise two key consequences of the disc embedding theorem. The chapter begins with an introduction to surgery theory from the perspective of 4-manifolds. In particular, the terms and maps in the surgery sequence are defined, and an explanation is given as to how the sphere embedding theorem, with the added ingredient of topological transversality, can be used to define the maps in the surgery sequence and show that it is exact. The surgery sequence is applied to classify simply connected closed 4-manifolds up to homeomorphism. The chapter closes with a survey of related classification results.

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