scholarly journals CIRCLE ACTIONS, CENTRAL EXTENSIONS AND STRING STRUCTURES

2010 ◽  
Vol 07 (06) ◽  
pp. 1065-1092 ◽  
Author(s):  
MICHAEL K. MURRAY ◽  
RAYMOND F. VOZZO
Keyword(s):  
Differential Form ◽  
Central Extensions ◽  
Circle Actions ◽  
The Real ◽  
Circle Bundles ◽  
String Class ◽  
Equivalence Of Categories ◽  
Bundle Gerbes

The caloron correspondence can be understood as an equivalence of categories between G-bundles over circle bundles and LG ⋊ρ S1-bundles where LG is the group of smooth loops in G. We use it, and lifting bundle gerbes, to derive an explicit differential form based formula for the (real) string class of an LG ⋊ρ S1-bundle.

Circle Actions

2020 ◽  
pp. 161-166
Author(s):  
Loring W. Tu
Keyword(s):  
Differential Form ◽  
Circle Action ◽  
Graded Algebra ◽  
Graded Algebras ◽  
Circle Actions ◽  
Algebra Isomorphism ◽  
Weil Algebra ◽  
Differential Graded Algebras ◽  
Cartan Model

This chapter focuses on circle actions. Specifically, it specializes the Weil algebra and the Weil model to a circle action. In this case, all the formulas simplify. The chapter derives a simpler complex, called the Cartan model, which is isomorphic to the Weil model as differential graded algebras. It considers the theorem that for a circle action, there is a graded-algebra isomorphism. Under the isomorphism F, the Weil differential δ‎ corresponds to a differential called the Cartan differential. An element of the Cartan model is called an equivariant differential form or equivariant form for a circle action on the manifold M.

scholarly journals Central Extensions of Lie Groups Preserving a Differential Form

2020 ◽  
Author(s):  
Tobias Diez ◽  
Bas Janssens ◽  
Karl-Hermann Neeb ◽  
Cornelia Vizman
Keyword(s):  
Lie Groups ◽  
Lie Algebra ◽  
Lie Group ◽  
Differential Form ◽  
Integral Form ◽  
Symplectic Manifolds ◽  
Central Extensions ◽  
Mapping Space ◽  
Canonical Class ◽  
Differential Characters

Abstract Let $M$ be a manifold with a closed, integral $(k+1)$-form $\omega $, and let $G$ be a Fréchet–Lie group acting on $(M,\omega )$. As a generalization of the Kostant–Souriau extension for symplectic manifolds, we consider a canonical class of central extensions of ${\mathfrak{g}}$ by ${\mathbb{R}}$, indexed by $H^{k-1}(M,{\mathbb{R}})^*$. We show that the image of $H_{k-1}(M,{\mathbb{Z}})$ in $H^{k-1}(M,{\mathbb{R}})^*$ corresponds to a lattice of Lie algebra extensions that integrate to smooth central extensions of $G$ by the circle group ${\mathbb{T}}$. The idea is to represent a class in $H_{k-1}(M,{\mathbb{Z}})$ by a weighted submanifold $(S,\beta )$, where $\beta $ is a closed, integral form on $S$. We use transgression of differential characters from $ S$ and $ M $ to the mapping space $ C^\infty (S, M) $ and apply the Kostant–Souriau construction on $ C^\infty (S, M) $.

scholarly journals Flat circle bundles, pullbacks, and the circle made discrete

2005 ◽  
Vol 2005 (21) ◽  
pp. 3487-3495 ◽  
Author(s):  
John Oprea ◽  
Daniel Tanré
Keyword(s):  
Lie Groups ◽  
Euler Class ◽  
Circle Bundle ◽  
The Real ◽  
Circle Bundles

We use basic homotopical methods applied to Lie groups made discrete to prove that the real Euler class of a circle bundle vanishes if and only if the bundle is flat.

scholarly journals LOOP GROUPS, STRING CLASSES AND EQUIVARIANT COHOMOLOGY

2011 ◽  
Vol 90 (1) ◽  
pp. 109-127 ◽  
Author(s):  
RAYMOND F. VOZZO
Keyword(s):  
Lie Group ◽  
Differential Form ◽  
Equivariant Cohomology ◽  
Loop Group ◽  
Characteristic Classes ◽  
Loop Groups ◽  
Compact Lie Group ◽  
String Class ◽  
String Classes ◽  
Odd Dimensions

AbstractWe give a classifying theory for LG-bundles, where LG is the loop group of a compact Lie group G, and present a calculation for the string class of the universal LG-bundle. We show that this class is in fact an equivariant cohomology class and give an equivariant differential form representing it. We then use the caloron correspondence to define (higher) characteristic classes for LG-bundles and to prove a result for characteristic classes for based loop groups for the free loop group. These classes have a natural interpretation in equivariant cohomology and we give equivariant differential form representatives for the universal case in all odd dimensions.

scholarly journals Leopoldt kernels and central extensions of algebraic number fields

1990 ◽  
Vol 120 ◽  
pp. 67-76 ◽  
Author(s):  
Katsuya Miyake
Keyword(s):  
Number Field ◽  
Algebraic Number ◽  
Unit Group ◽  
Algebraic Number Field ◽  
Number Fields ◽  
Prime Divisors ◽  
Finite Degree ◽  
Algebraic Number Fields ◽  
Central Extensions ◽  
The Real

Let k be an algebraic number field of finite degree, and p be a fixed rational prime. We denote the set of all the non-Archimedian prime divisors of k by S0(k) and the set of all the real Archimedian ones by (k). Put and S = S0 ∪ S∞, and define a subgroup of the unit group (k) of k by

scholarly journals Geometries of Orthogonal Groups and their Contractions: A Unified Classical Deformation Viewpoint

1997 ◽  
Vol 12 (01) ◽  
pp. 99-107 ◽  
Author(s):  
M. Santander ◽  
F. J. Herranz
Keyword(s):  
Common Point ◽  
Point Of View ◽  
Orthogonal Groups ◽  
Central Extensions ◽  
The Real

The geometries of spaces having as groups the real orthogonal groups and some of their contractions are described from a common point of view. Their central extensions and Casimirs are explicitly given. An approach to the trigonometry of their spaces is also advanced.

scholarly journals Infinite families of inequivalent real circle actions on affine four-space

2019 ◽  
Vol Volume 3 ◽  
Author(s):  
Lucy Moser-Jauslin
Keyword(s):  
Fixed Point ◽  
Vector Bundles ◽  
Circle Action ◽  
Real Form ◽  
Circle Actions ◽  
New Approach ◽  
The Real ◽  
Nous Permet ◽  
International Audience ◽  
Real Forms

International audience The main result of this article is to construct infinite families of non-equivalent equivariant real forms of linear C*-actions on affine four-space. We consider the real form of $\mathbb{C}^*$ whose fixed point is a circle. In [F-MJ] one example of a non-linearizable circle action was constructed. Here, this result is generalized by developing a new approach which allows us to compare different real forms. The constructions of these forms are based on the structure of equivariant $\mathrm{O}_2(\mathbb{C})$-vector bundles. Le résultat principal de cet article est de construire des familles infinies de formes réelles équivariantes, non équivalentes entre elles, d’actions linéaires de $\mathbb{C}^*$ sur l’espace affine de dimension 4. L’article [F-MJ] construisait un exemple d’action du cercle non linéarisable. Ici nous généralisons ce résultat en développant une nouvelle approche qui nous permet de comparer les différentes formes réelles. Les constructions de ces formes réelles s’appuient sur la structure de $\mathrm{O}_2(\mathbb{C})$-fibrés vectoriels équivariants.

Scanning electron microscopy of human iliac bone by a simple preparation method

1990 ◽  
Vol 48 (3) ◽  
pp. 226-227
Author(s):  
Toshihiko Takita ◽  
Tomonori Naguro ◽  
Toshio Kameie ◽  
Akihiro Iino ◽  
Kichizo Yamamoto
Keyword(s):  
Electron Microscopy ◽  
Scanning Electron Microscopy ◽  
Preparation Method ◽  
Specimen Preparation ◽  
Real Surface ◽  
Public Attention ◽  
Preparation Methods ◽  
The Real ◽  
Simple Preparation ◽  
Scanning Electron

Recently with the increase in advanced age population, the osteoporosis becomes the object of public attention in the field of orthopedics. The surface topography of the bone by scanning electron microscopy (SEM) is one of the most useful means to study the bone metabolism, that is considered to make clear the mechanism of the osteoporosis. Until today many specimen preparation methods for SEM have been reported. They are roughly classified into two; the anorganic preparation and the simple preparation. The former is suitable for observing mineralization, but has the demerit that the real surface of the bone can not be observed and, moreover, the samples prepared by this method are extremely fragile especially in the case of osteoporosis. On the other hand, the latter has the merit that the real information of the bone surface can be obtained, though it is difficult to recognize the functional situation of the bone.

Personal Audio System: Hearing Symptoms, Habits, and Sound Pressure Levels Measured in Real Ear and a Manikin

2020 ◽  
Vol 63 (6) ◽  
pp. 2016-2026
Author(s):  
Tamara R. Almeida ◽  
Clayton H. Rocha ◽  
Camila M. Rabelo ◽  
Raquel F. Gomes ◽  
Ivone F. Neves-Lobo ◽  
...  
Keyword(s):  
Sound Pressure ◽  
Daily Basis ◽  
Cross Sectional Study ◽  
Normal Hearing ◽  
Chi Square ◽  
Cross Sectional ◽  
The Real ◽  
Significant Difference ◽  
Sound Pressure Levels ◽  
Audio System

Purpose The aims of this study were to characterize hearing symptoms, habits, and sound pressure levels (SPLs) of personal audio system (PAS) used by young adults; estimate the risk of developing hearing loss and assess whether instructions given to users led to behavioral changes; and propose recommendations for PAS users. Method A cross-sectional study was performed in 50 subjects with normal hearing. Procedures included questionnaire and measurement of PAS SPLs (real ear and manikin) through the users' own headphones and devices while they listened to four songs. After 1 year, 30 subjects answered questions about their usage habits. For the statistical analysis, one-way analysis of variance, Tukey's post hoc test, Lin and Spearman coefficients, the chi-square test, and logistic regression were used. Results Most subjects listened to music every day, usually in noisy environments. Sixty percent of the subjects reported hearing symptoms after using a PAS. Substantial variability in the equivalent music listening level (Leq) was noted ( M = 84.7 dBA; min = 65.1 dBA, max = 97.5 dBA). A significant difference was found only in the 4-kHz band when comparing the real-ear and manikin techniques. Based on the Leq, 38% of the individuals exceeded the maximum daily time allowance. Comparison of the subjects according to the maximum allowed daily exposure time revealed a higher number of hearing complaints from people with greater exposure. After 1 year, 43% of the subjects reduced their usage time, and 70% reduced the volume. A volume not exceeding 80% was recommended, and at this volume, the maximum usage time should be 160 min. Conclusions The habit of listening to music at high intensities on a daily basis seems to cause hearing symptoms, even in individuals with normal hearing. The real-ear and manikin techniques produced similar results. Providing instructions on this topic combined with measuring PAS SPLs may be an appropriate strategy for raising the awareness of people who are at risk. Supplemental Material https://doi.org/10.23641/asha.12431435

Sign in / Sign up

Export Citation Format

Share Document