scholarly journals Commutativeness of Fundamental Groups of Topological Groups

2013 ◽  
Vol 21 (2) ◽  
pp. 127-131
Author(s):  
Artur Korniłowicz
Keyword(s):  
Fundamental Groups ◽  
Topological Groups

Summary In this article we prove that fundamental groups based at the unit point of topological groups are commutative [11].

Filling words in fundamental groups of Riemann surfaces

2013 ◽  
Vol 50 (1) ◽  
pp. 31-50
Author(s):  
C. Zhang
Keyword(s):  
Riemann Surface ◽  
Fundamental Group ◽  
Riemann Surfaces ◽  
Fundamental Groups ◽  
Closed Geodesics ◽  
New Words

The purpose of this article is to utilize some exiting words in the fundamental group of a Riemann surface to acquire new words that are represented by filling closed geodesics.

QUALITATIVE CHANGES IN RHYTHMIC GYMNASTICS HOOP THROWS FROM THE PERSPECTIVE OF BIOMECHANICAL ANALYSIS

2020 ◽  
pp. 1-8
Author(s):  
Raluca Tanasa
Keyword(s):  
Correlation Coefficient ◽  
Video Recording ◽  
Biomechanical Analysis ◽  
Fundamental Groups ◽  
Horizontal Distance ◽  
Video Recordings ◽  
Rhythmic Gymnastics ◽  
Female Gymnasts ◽  
Execution Technique ◽  
Qualitative Changes

Throws and catches in rhythmic gymnastics represent one of the fundamental groups of apparatus actuation. They represent for the hoop actions of great showmanship, but also elements of risk. The purpose of this paper is to improve the throw execution technique through biomechanical analysis in order to increase the performance of female gymnasts in competitions. The subjects of this study were 8 gymnasts aged 9-10 years old, practiced performance Rhythmic Gymnastics. The experiment consisted in video recording and the biomechanical analysis of the element “Hoop throw, step jump and catch”. After processing the video recordings using the Simi Motion software, we have calculated and obtained values concerning: launch height, horizontal distance and throwing angle between the arm and the horizontal. Pursuant to the data obtained, we have designed a series of means to improve the execution technique for the elements comprised within the research and we have implemented them in the training process. Regarding the interpretation of the results, it may be highlighted as follows: height and horizontal distance in this element have values of the correlation coefficient of 0.438 and 0.323, thus a mean significance of 0.005. The values of the arm/horizontal angle have improved for all the gymnasts, the correlation coefficient being 0.931, with a significance of 0.01. As a general conclusion, after the results obtained, it may be stated that the means introduced in the experiment have proven their efficacy, which has led to the optimisation of the execution technique, thus confirming the research hypothesis.

SOME PROPERTIES OF G-SPACES ACTED WITH TOPOLOGICAL GROUPS

2020 ◽  
Vol 9 (7) ◽  
pp. 4917-4922
Author(s):  
S. Sivakumar ◽  
D. Lohanayaki
Keyword(s):  
Topological Groups

scholarly journals Exploring the landscape of CHL strings on Td

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Anamaría Font ◽  
Bernardo Fraiman ◽  
Mariana Graña ◽  
Carmen A. Núñez ◽  
Héctor Parra De Freitas
Keyword(s):  
Gauge Group ◽  
Moduli Space ◽  
Dynkin Diagram ◽  
Fundamental Groups ◽  
Computer Algorithms ◽  
Abelian Gauge ◽  
Reduced Rank ◽  
Systematic Exploration ◽  
String Models ◽  
Simply Connected

Abstract Compactifications of the heterotic string on special Td/ℤ2 orbifolds realize a landscape of string models with 16 supercharges and a gauge group on the left-moving sector of reduced rank d + 8. The momenta of untwisted and twisted states span a lattice known as the Mikhailov lattice II(d), which is not self-dual for d > 1. By using computer algorithms which exploit the properties of lattice embeddings, we perform a systematic exploration of the moduli space for d ≤ 2, and give a list of maximally enhanced points where the U(1)d+8 enhances to a rank d + 8 non-Abelian gauge group. For d = 1, these groups are simply-laced and simply-connected, and in fact can be obtained from the Dynkin diagram of E10. For d = 2 there are also symplectic and doubly-connected groups. For the latter we find the precise form of their fundamental groups from embeddings of lattices into the dual of II(2). Our results easily generalize to d > 2.

scholarly journals CONTINUITY OF MEASURABLE HOMOMORPHISMS

2008 ◽  
Vol 78 (1) ◽  
pp. 171-176 ◽  
Author(s):  
JANUSZ BRZDȨK
Keyword(s):  
Topological Group ◽  
Abelian Group ◽  
Baire Property ◽  
Topological Groups ◽  
Locally Compact ◽  
Compact Topological Group ◽  
Locally Compact Topological Group

AbstractWe give some general results concerning continuity of measurable homomorphisms of topological groups. As a consequence we show that a Christensen measurable homomorphism of a Polish abelian group into a locally compact topological group is continuous. We also obtain similar results for the universally measurable homomorphisms and the homomorphisms that have the Baire property.

On the Dimension Modulo Classes of Topological Spaces and Free Topological Groups

2003 ◽  
Vol 10 (2) ◽  
pp. 209-222
Author(s):  
I. Bakhia
Keyword(s):  
Wide Class ◽  
Sufficient Conditions ◽  
Topological Spaces ◽  
Topological Groups ◽  
Compact Spaces ◽  
Topological Semigroups

Abstract Functions of dimension modulo a (rather wide) class of spaces are considered and the conditions are found, under which the dimension of the product of spaces modulo these classes is equal to zero. Based on these results, the sufficient conditions are established, under which spaces of free topological semigroups (in the sense of Marxen) and spaces of free topological groups (in the sense of Markov and Graev) are zero-dimensional modulo classes of compact spaces.

scholarly journals Schottky groups acting on homogeneous rational manifolds

2019 ◽  
Vol 2019 (753) ◽  
pp. 23-56 ◽  
Author(s):  
Christian Miebach ◽  
Karl Oeljeklaus
Keyword(s):  
Deformation Theory ◽  
Group Actions ◽  
Picard Group ◽  
Schottky Group ◽  
Fundamental Groups ◽  
Complex Manifolds ◽  
Schottky Groups ◽  
Algebraic Dimension ◽  
Geometric Invariants ◽  
Compact Complex Manifolds

AbstractWe systematically study Schottky group actions on homogeneous rational manifolds and find two new families besides those given by Nori’s well-known construction. This yields new examples of non-Kähler compact complex manifolds having free fundamental groups. We then investigate their analytic and geometric invariants such as the Kodaira and algebraic dimension, the Picard group and the deformation theory, thus extending results due to Lárusson and to Seade and Verjovsky. As a byproduct, we see that the Schottky construction allows to recover examples of equivariant compactifications of {{\rm{SL}}(2,\mathbb{C})/\Gamma} for Γ a discrete free loxodromic subgroup of {{\rm{SL}}(2,\mathbb{C})}, previously obtained by A. Guillot.

Sign in / Sign up

Export Citation Format

Share Document