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Betti Numbers of the Moduli Space of Rank 3 Parabolic Higgs Bundles
Parabolic Higgs bundles on a Riemann surface are of interest for many reasons, one of them being their importance in the study of representations of the fundamental group of the punctured surface in the complex general linear group. In this paper the authors calculate the Betti numbers of the moduli space of rank 3 parabolic Higgs bundles with fixed and non-fixed determinant, using Morse theory. A key point is that certain critical submanifolds of the Morse function can be identified with moduli spaces of parabolic triples. These moduli spaces come in families depending on a real parameter and the authors carry out a careful analysis of them by studying their variation with this parameter. Thus the authors obtain in particular information about the topology of the moduli spaces of parabolic triples for the value of the parameter relevant to the study of parabolic Higgs bundles. The remaining critical submanifolds are also described: one of them is the moduli space of parabolic bundles, while the rem
Betti Numbers of the Moduli Space of Rank 3 Parabolic Higgs Bundles
Parabolic Higgs bundles on a Riemann surface are of interest for many reasons, one of them being their importance in the study of representations of the fundamental group of the punctured surface in the complex general linear group. In this paper the authors calculate the Betti numbers of the moduli space of rank 3 parabolic Higgs bundles with fixed and non-fixed determinant,
Dying Prepared in Medieval and Early Modern Northern Europe
Dying Prepared in Medieval and Early Modern Northern Europe offers an analysis of the various ways in which people made preparations for death in medieval and early modern Northern Europe.
The Cambridge Guide to the Worlds of Shakespeare
This transhistorical, international and interdisciplinary work will be of interest to students, theater professionals and Shakespeare scholars.
Calculus With Applications
Burstein, and Lax's Calculus with Applications and Computing offers meaningful explanations of the important theorems of single variable calculus. Written with students in mathematics, the physical sciences, and engineering in mind, and revised with their help, it shows that the themes of calculation, approximation, and modeling are central to mathematics and the main ideas of single variable calculus. This edition brings the innovation of the first edition to a new generation of students. New sections in this book use simple, elementary examples to show that when applying calculus concepts to approximations of functions, uniform convergence is more natural and easier to use than point-wise convergence. As in the original, this edition includes material that is essential for students in science and engineering, including an elementary introduction to complex numbers and complex-valued functions, applications of calculus to modeling vibrations and population dynamics, and an introduction to probability and information theory.
Human Rights in the Digital Age
The digital age began in 1939 with the construction of the first digital computer. In the sixty-five years that have followed, the influence of digitisation on our everyday lives has grown steadily and today digital technology has a greater influence on our lives than at any time since its development. This book examines the role played by digital technology in both the exercise and suppression of human rights. The global digital environment has allowed us to reinterpret the concept of universal human rights. Discourse on human rights need no longer be limited by national or cultural boundaries and individuals have the ability to create new forms in which to exercise their rights or even to ...
