Twists And Curves

Written in response to the many requests for a practical and accessible guide to exercise for scoliosis sufferers, Curves, Twists and Bends combines the experience of Annette Wellings, who has major scoliosis, with that of Alan Herdman, the UK's leading Pilates teacher. This clear and concise book explains what scoliosis is, its symptoms, and its physical and psychological impact. It includes a series of Pilates exercises, designed by the authors specifically to promote flexibility, posture and muscle strength in scoliosis sufferers, and also vital information on what exercises to avoid. It offers basic strategies and practical tips for living with the condition, including useful advice on diet, rest, sitting, carrying and how to dress. Written with the full range of scoliosis sufferers in mind, Pilates for Scoliosis emphasises the importance and feasibility of gentle exercise for keeping the body as healthy and flexible as possible. Curves, Twists and Bends: A Practical Guide to Pilates for Scoliosis will be indispensible to individuals with scoliosis and their families as well as to physical therapists, Pilates instructors and other professionals who advise scoliosis patients on exercise and lifestyle options.

These notes introduce a new class of algebraic curves on Hilbert modular surfaces. These curves are called twisted Teichmüller curves, because their construction is very reminiscent of Hirzebruch-Zagier cycles. These new objects are analyzed in detail and their main properties are described. In particular, the volume of twisted Teichmüller curves is calculated and their components are partially classified. The study of algebraic curves on Hilbert modular surfaces has been widely covered in the literature due to their arithmetic importance. Among these, twisted diagonals (Hirzebruch-Zagier cycles) are some of the most important examples.

This book constitutes the refereed proceedings of the 11th IMA International Conference on Cryptography and Coding, held in Cirencester, UK in December 2007. The 22 revised full papers presented together with two invited contributions were carefully reviewed and selected from 48 submissions. The papers are organized in topical sections on signatures, boolean functions, block cipher cryptanalysis, side channels, linear complexity, public key encryption, curves, and RSA implementation.

The study of the mapping class group Mod(S) is a classical topic that is experiencing a renaissance. It lies at the juncture of geometry, topology, and group theory. This book explains as many important theorems, examples, and techniques as possible, quickly and directly, while at the same time giving full details and keeping the text nearly self-contained. The book is suitable for graduate students. A Primer on Mapping Class Groups begins by explaining the main group-theoretical properties of Mod(S), from finite generation by Dehn twists and low-dimensional homology to the Dehn-Nielsen-Baer theorem. Along the way, central objects and tools are introduced, such as the Birman exact sequence, the complex of curves, the braid group, the symplectic representation, and the Torelli group. The book then introduces Teichmüller space and its geometry, and uses the action of Mod(S) on it to prove the Nielsen-Thurston classification of surface homeomorphisms. Topics include the topology of the moduli space of Riemann surfaces, the connection with surface bundles, pseudo-Anosov theory, and Thurston's approach to the classification.

Strip Piecing With Twists and Turns! Start with basic strip piecing, add easy and gently curved edges, and prepare to be amazed! Louisa introduces 4 design concepts, 2 template based and 2 template free, all with step-by-step instructions. Whether you own Louisa’s 2001 best-selling Strips ‘n Curves or you’re new to the world of combining curved-edge and strip piecing, you’ll love the fresh ideas and fabulous inspiration in this book. Learn Louisa’s four new techniques (Half Clamshell, Free-Form Curves, Strips ‘n Circles, and The Swirl); then try them in four complete project quilts! Lots of step-bystep photos and clear instructions ensure your success. Ideas for home décor, garments, and quilts, quilts, quilts!

This unique reference, aimed at research topologists, gives an exposition of the 'pseudo-Anosov' theory of foliations of 3-manifolds. This theory generalizes Thurston's theory of surface automorphisms and reveals an intimate connection between dynamics, geometry and topology in 3 dimensions. Significant themes returned to throughout the text include the importance of geometry, especially the hyperbolic geometry of surfaces, the importance of monotonicity, especially in 1-dimensional and co-dimensional dynamics, and combinatorial approximation, using finite combinatorical objects such as train-tracks, branched surfaces and hierarchies to carry more complicated continuous objects.

The work of Max Dehn (1878-1952) has been quietly influential in mathematics since the beginning of the 20th century. In 1900 he became the first to solve one of the famous Hilbert problems (the third, on the decomposition of polyhedra), in 1907 he collaborated with Heegaard to produce the first survey of topology, and in 1910 he began publishing his own investigations in topology and combinatorial group theory. His influence is apparent in the terms Dehn's algorithm, Dehn's lemma and Dehn surgery (and Dehnsche Gruppenbilder, generally known in English as Cayley diagrams), but direct access to his work has been difficult. No edition of his works has been produced, and some of his most important results were never published, at least not by him. The present volume is a modest attempt to bring Dehn's work to a wider audience, particularly topologists and group theorists curious about the origins of their subject and interested in mining the sources for new ideas. It consists of English translations of eight works : five of Dehn's major papers in topology and combinatorial group theory, and three unpublished works which illuminate the published papers and contain some results not available elsewhere. In addition, I have written a short introduction to each work, summarising its contents and trying to establish its place among related works of Dehn and others, and I have added an appendix on the Dehn-Nielsen theorem (often known simply as Nielsen's theorem) .

In addition, attention is paid to the algebraic and Lie-theoretic applications of Clifford algebras---particularly their intersection with Hopf algebras, Lie algebras and representations, graded algebras, and associated mathematical structures. Symplectic Clifford algebras are also discussed. Finally, Clifford algebras play a strong role in both physics and engineering. The physics section features an investigation of geometric algebras, chiral Dirac equations, spinors and Fermions, and applications of Clifford algebras in classical mechanics and general relativity. Twistor and octonionic methods, electromagnetism and gravity, elementary particle physics, noncommutative physics, Dirac's equation, quantum spheres, and the Standard Model are among topics considered at length.