Some plane curves whose complements have non-abelian fundamental groups

1975 ◽  
Vol 218 (1) ◽  
pp. 55-65 ◽  
Author(s):  
Mutsuo Oka
Keyword(s):  
Plane Curves ◽  
Fundamental Groups

scholarly journals Fundamental groups of complements of plane curves and symplectic invariants

Topology ◽  
2004 ◽  
Vol 43 (6) ◽  
pp. 1285-1318 ◽  
Author(s):  
D. Auroux ◽  
S.K. Donaldson ◽  
L. Katzarkov ◽  
M. Yotov
Keyword(s):  
Plane Curves ◽  
Fundamental Groups ◽  
Symplectic Invariants

Fundamental groups of a class of rational cuspidal plane curves

2016 ◽  
Vol 27 (12) ◽  
pp. 1650104
Author(s):  
A. Muhammed Uludağ
Keyword(s):  
Projective Plane ◽  
Plane Curves ◽  
Fundamental Groups ◽  
Cremona Transformations ◽  
Group Presentations ◽  
Abelian Subgroups

We compute the presentations of fundamental groups of the complements of a class of rational cuspidal projective plane curves classified by Flenner, Zaidenberg, Fenske and Saito. We use the Zariski–Van Kampen algorithm and exploit the Cremona transformations used in the construction of these curves. We simplify and study the group presentations so obtained and determine if they are abelian, finite or big, i.e. if they contain free non-abelian subgroups. We also study the quotients of these groups to some extent.

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.

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