scholarly journals Projective crystalline representations of étale fundamental groups and twisted periodic Higgs–de Rham flow

2021 ◽  
Author(s):  
Ruiran Sun ◽  
Jinbang Yang ◽  
Kang Zuo
Keyword(s):  
Fundamental Groups ◽  
Crystalline Representations ◽  
De Rham

scholarly journals Rigidity of lattices of non-positive curvature

1983 ◽  
Vol 3 (1) ◽  
pp. 47-85 ◽  
Author(s):  
P. Eberlein
Keyword(s):  
Symmetric Space ◽  
Sectional Curvature ◽  
Positive Curvature ◽  
Fundamental Groups ◽  
Positive Sectional Curvature ◽  
Constant Multiple ◽  
De Rham

AbstractLet M, M* denote compact, connected manifolds of non-positive sectional curvature whose fundamental groups are isomorphic and whose Euclidean de Rham factors are trivial. We prove that: if M is a compact irreducible quotient of a reducible symmetric space H, then M and M* are isometric up to a constant multiple of the metric; and that the number and dimensions of the local de Rham factors are the same for M and M*. Gromov has independently proved the first result in the more general case that M is locally symmetric and globally irreducible with rank at least two.

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.

THE DE RHAM COHOMOLOGY OF DIFFERENTIAL SPACES

1989 ◽  
Vol 22 (1) ◽  
pp. 249-272 ◽  
Author(s):  
Wiesław Sasin
Keyword(s):  
De Rham Cohomology ◽  
De Rham ◽  
Differential Spaces

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.

scholarly journals On the Voevodsky motive of the moduli space of Higgs bundles on a curve

2021 ◽  
Vol 27 (1) ◽  
Author(s):  
Victoria Hoskins ◽  
Simon Pepin Lehalleur
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Characteristic Zero ◽  
Rational Point ◽  
Triangulated Category ◽  
Higgs Bundles ◽  
Projective Curve ◽  
Smooth Projective Curve ◽  
De Rham

AbstractWe study the motive of the moduli space of semistable Higgs bundles of coprime rank and degree on a smooth projective curve C over a field k under the assumption that C has a rational point. We show this motive is contained in the thick tensor subcategory of Voevodsky’s triangulated category of motives with rational coefficients generated by the motive of C. Moreover, over a field of characteristic zero, we prove a motivic non-abelian Hodge correspondence: the integral motives of the Higgs and de Rham moduli spaces are isomorphic.

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 Counterexamples to Hochschild-Kostant-Rosenberg in characteristic p

2021 ◽  
Vol 9 ◽  
Author(s):  
Benjamin Antieau ◽  
Bhargav Bhatt ◽  
Akhil Mathew
Keyword(s):  
Spectral Sequence ◽  
Spectral Sequences ◽  
Characteristic P ◽  
De Rham

Abstract We give counterexamples to the degeneration of the Hochschild-Kostant-Rosenberg spectral sequence in characteristic p, both in the untwisted and twisted settings. We also prove that the de Rham-HP and crystalline-TP spectral sequences need not degenerate.

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