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Relevant bibliographies by topics / Hurwitz's Automorphism Theorem

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Academic literature on the topic 'Hurwitz's Automorphism Theorem'

Author: Grafiati

Published: 4 June 2021

Last updated: 7 September 2023

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Journal articles on the topic "Hurwitz's Automorphism Theorem"

1

MORIFUJI, TAKAYUKI. "A VANISHING THEOREM FOR THE -INVARIANT AND HURWITZ GROUPS." Nagoya Mathematical Journal 228 (October 20, 2016): 114–23. http://dx.doi.org/10.1017/nmj.2016.55.

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In this paper we discuss a relationship between the spectral asymmetry and the surface symmetry. More precisely, we show that for every automorphism of a Hurwitz surface with the automorphism group $\text{PSL}(2,\mathbb{F}_{q})$, the $\unicode[STIX]{x1D702}$-invariant of the corresponding mapping torus vanishes if $q$ is sufficiently large.

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2

Zomorrodian, Reza. "Classification of p-groups of automorphisms of Riemann surfaces and their lower central series." Glasgow Mathematical Journal 29, no. 2 (1987): 237–44. http://dx.doi.org/10.1017/s0017089500006881.

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In a previous paper [7], I have made a study of the ”nilpotent” analogue of Hurwitz theorem [4] by considering a particular family of signatures called ”nilpotent admissible” [5]. We saw however, that if μN(g) represents the order of the largest nilpotent group of automorphisms of a surface of genus g < 2, then μN(g) < 16(g − 1) and this upper bound occurs when the covering group is a triangle group having the signature (0; 2,4,8) which is in its own 2-local formThe restriction to the nilpotent groups enabled me to obtain much more precise information than was available in the general ca

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3

Greene, Robert E. "Orbifolds, the Regular Solids, and Hurwitz’s 84(g – 1) Theorem." Journal of Geometric Analysis 33, no. 7 (2023). http://dx.doi.org/10.1007/s12220-023-01251-8.

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AbstractThis paper presents an exposition of the analysis via orbifolds of the isometries with isolated fixed points of compact surfaces, giving a view of the classification of the five regular solids, following the treatment by William Thurston. Then it is shown that a closely related method can be used to recover the classical theorem of Hurwitz that the group of holomorphic automorphisms of a compact Riemann surface of genus $$g>1$$ g > 1 has order at most $$84(g-1)$$ 84 ( g - 1 ) .

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Dissertations / Theses on the topic "Hurwitz's Automorphism Theorem"

1

Ram, Mohan Devang S. "An Introduction to Minimal Surfaces." Thesis, 2014. http://etd.iisc.ac.in/handle/2005/2890.

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In the first chapter of this report, our aim is to introduce harmonic maps between Riemann surfaces using the Energy integral of a map. Once we have the desired prerequisites, we move on to show how to continuously deform a given map to a harmonic map (i.e., find a harmonic map in its homotopy class). We follow J¨urgen Jost’s approach using classical potential theory techniques. Subsequently, we analyze the additional conditions needed to ensure a certain uniqueness property of harmonic maps within a given homotopy class. In conclusion, we look at a couple of applications of what we have shown

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2

Ram, Mohan Devang S. "An Introduction to Minimal Surfaces." Thesis, 2014. http://etd.iisc.ernet.in/handle/2005/2890.

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In the first chapter of this report, our aim is to introduce harmonic maps between Riemann surfaces using the Energy integral of a map. Once we have the desired prerequisites, we move on to show how to continuously deform a given map to a harmonic map (i.e., find a harmonic map in its homotopy class). We follow J¨urgen Jost’s approach using classical potential theory techniques. Subsequently, we analyze the additional conditions needed to ensure a certain uniqueness property of harmonic maps within a given homotopy class. In conclusion, we look at a couple of applications of what we have shown

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