Periods of Abelian Differentials With Prescribed Singularities

2020 ◽  
Author(s):  
Thomas Le Fils
Keyword(s):  
Fundamental Group ◽  
Closed Surface ◽  
Translation Surface ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Conical Singularities ◽  
Abelian Differentials ◽  
Necessary And Sufficient

Abstract We give a necessary and sufficient condition for a representation of the fundamental group of a closed surface of genus at least $2$ to ${\mathbb{C}}$ to be the holonomy of a translation surface with a prescribed list of conical singularities. Equivalently, we determine the period maps of abelian differentials with prescribed list of multiplicities of zeros. Our main result was also obtained, independently, by Bainbridge, Johnson, Judge, and Park.

Surfaces Embedded in M2 × S1

1970 ◽  
Vol 22 (3) ◽  
pp. 553-568 ◽  
Author(s):  
William Jaco
Keyword(s):  
Simple Closed Curve ◽  
Closed Surface ◽  
Closed Curve ◽  
Natural Projection ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Covering Projection ◽  
Ambient Isotopy ◽  
Necessary And Sufficient

In this paper we study incompressible and injective (see § 2 for definitions) surfaces embedded in M2 × S1, where M2 is a surface and S1 is the 1-sphere. We are able to characterize embeddings which are incompressible in M2 × S1 when M2 is closed and orientable. Namely, a necessary and sufficient condition for the closed surface F to be incompressible in M2 × S1, where M2is closed and orientable, is that there exists an ambient isotopy ht, 0 ≦ t ≦ 1, of M2 × S1onto itself so that either(i) there is a non-trivial simple closed curve J ⊂ M2 and h1(F) = J × S1, or(ii) p\h1(F) is a covering projection of h1(F) onto M2, where p is the natural projection of M2 × S1onto M2.

scholarly journals Entropy and semi-conjugacy in dimension two

1988 ◽  
Vol 8 (4) ◽  
pp. 585-596 ◽  
Author(s):  
Michael Handel
Keyword(s):  
Topological Entropy ◽  
Closed Surface ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient

AbstractWe prove that if a diffeomorphism f of a closed surface is homotopic to and has the same topological entropy as a pseudo-Anosov homeomorphism g, then f is semi-conjugate to g. As part of the proof, a necessary and sufficient condition is given for a pseudo-orbit of a pseudo-Anosov homeomorphism g to be shadowed by an actual orbit of g.

A Proposed Framework Emphasizing Auditor Reliability over Auditor Independence

2003 ◽  
Vol 17 (3) ◽  
pp. 257-266 ◽  
Author(s):  
Mark H. Taylor ◽  
F. Todd DeZoort ◽  
Edward Munn ◽  
Martha Wetterhall Thomas
Keyword(s):  
Public Interest ◽  
Auditor Independence ◽  
Public Confidence ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Accounting Profession ◽  
The Public ◽  
Necessary And Sufficient

This paper introduces an auditor reliability framework that repositions the role of auditor independence in the accounting profession. The framework is motivated in part by widespread confusion about independence and the auditing profession's continuing problems with managing independence and inspiring public confidence. We use philosophical, theoretical, and professional arguments to argue that the public interest will be best served by reprioritizing professional and ethical objectives to establish reliability in fact and appearance as the cornerstone of the profession, rather than relationship-based independence in fact and appearance. This revised framework requires three foundation elements to control subjectivity in auditors' judgments and decisions: independence, integrity, and expertise. Each element is a necessary but not sufficient condition for maximizing objectivity. Objectivity, in turn, is a necessary and sufficient condition for achieving and maintaining reliability in fact and appearance.

The Power of Public Positions

2018 ◽  
Author(s):  
Thomas Sinclair
Keyword(s):  
Detailed Analysis ◽  
Political Authority ◽  
The State ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
State Institutions ◽  
State Of Nature ◽  
Necessary And Sufficient

The Kantian account of political authority holds that the state is a necessary and sufficient condition of our freedom. We cannot be free outside the state, Kantians argue, because any attempt to have the “acquired rights” necessary for our freedom implicates us in objectionable relations of dependence on private judgment. Only in the state can this problem be overcome. But it is not clear how mere institutions could make the necessary difference, and contemporary Kantians have not offered compelling explanations. A detailed analysis is presented of the problems Kantians identify with the state of nature and the objections they face in claiming that the state overcomes them. A response is sketched on behalf of Kantians. The key idea is that under state institutions, a person can make claims of acquired right without presupposing that she is by nature exceptional in her capacity to bind others.

scholarly journals Lorentz Boosts and Wigner Rotations: Self-Adjoint Complexified Quaternions

Physics ◽  
2021 ◽  
Vol 3 (2) ◽  
pp. 352-366
Author(s):  
Thomas Berry ◽  
Matt Visser
Keyword(s):  
Point Of View ◽  
Sufficient Condition ◽  
Use Of Self ◽  
Necessary And Sufficient Condition ◽  
Wigner Rotation ◽  
Inertial Frames ◽  
Explicit Formulae ◽  
Specific Implementation ◽  
Necessary And Sufficient ◽  
Lorentz Boosts

In this paper, Lorentz boosts and Wigner rotations are considered from a (complexified) quaternionic point of view. It is demonstrated that, for a suitably defined self-adjoint complex quaternionic 4-velocity, pure Lorentz boosts can be phrased in terms of the quaternion square root of the relative 4-velocity connecting the two inertial frames. Straightforward computations then lead to quite explicit and relatively simple algebraic formulae for the composition of 4-velocities and the Wigner angle. The Wigner rotation is subsequently related to the generic non-associativity of the composition of three 4-velocities, and a necessary and sufficient condition is developed for the associativity to hold. Finally, the authors relate the composition of 4-velocities to a specific implementation of the Baker–Campbell–Hausdorff theorem. As compared to ordinary 4×4 Lorentz transformations, the use of self-adjoint complexified quaternions leads, from a computational view, to storage savings and more rapid computations, and from a pedagogical view to to relatively simple and explicit formulae.

Sign in / Sign up

Export Citation Format

Share Document