The recent introduction of the Seiberg-Witten invariants of smooth four-manifolds has revolutionized the study of those manifolds. The invariants are gauge-theoretic in nature and are close cousins of the much-studied SU(2)-invariants defined over fifteen years ago by Donaldson. On a practical level, the new invariants have proved to be more powerful and have led to a vast generalization of earlier results. This book is an introduction to the Seiberg-Witten invariants. The work begins with a review of the classical material on Spin c structures and their associated Dirac operators. Next comes a discussion of the Seiberg-Witten equations, which is set in the context of nonlinear elliptic operators on an appropriate infinite dimensional space of configurations. It is demonstrated that the space of solutions to these equations, called the Seiberg-Witten moduli space, is finite dimensional, and its dimension is then computed. In contrast to the SU(2)-case, the Seiberg-Witten moduli spaces are shown to be compact. The Seiberg-Witten invariant is then essentially the homology class in the space of configurations represented by the Seiberg-Witten moduli space. The last chapter gives a flavor for the applications of these new invariants by computing the invariants for most Kahler surfaces and then deriving some basic toological consequences for these surfaces.
This annotated Civil War memoir provides a detailed account of General Morgan’s famous battles and raids from a Confederate soldier’s perspective. John Marion Porter grew up working at his family's farm and dry goods store in Butler County, Kentucky. He was studying to become a lawyer when the Civil War began. As the son of a family of slave owners, Porter identified with the Southern cause and quickly enlisted in the Confederate army. He and his lifelong friend Thomas Henry Hines served in the Ninth Kentucky Calvary under John Hunt Morgan, the “Thunderbolt of the Confederacy.” When the war ended, Porter began writing detailed memoirs of his experiences during the war years, including tales of scouting behind enemy lines, sabotaging a Union train, being captured and held as a prisoner of war, and searching for an army to join after his release. Editor Kent Masterson Brown spent several years preparing Porter's memoir for publication, clarifying details and adding annotations to provide historical context. One of Morgan's Men is a fascinating firsthand account of the life of a Confederate soldier.
Reprint of the original, first published in 1873. The publishing house Anatiposi publishes historical books as reprints. Due to their age, these books may have missing pages or inferior quality. Our aim is to preserve these books and make them available to the public so that they do not get lost.
Sherman: A Soldier’s Passion for Order is the premier biography of William Tecumseh Sherman, the Civil War commander known for his “destructive war” policy against Confederates and as a consummate soldier. This updated edition of John F. Marszalek’s award-winning book presents the general as a complicated man who, fearing anarchy, searched for the order that he hoped would make his life a success. Sherman was profoundly influenced by the death of his father and his subsequent relationship with the powerful Whig politician Thomas Ewing and his family. Although the Ewings treated Sherman as one of their own, the young Sherman was determined to make it on his own. He graduated from West Point and moved on to service at military posts throughout the South. This volume traces Sherman’s involvement in the Mexican War in the late 1840s, his years battling prospectors and deserting soldiers in gold-rush California, and his 1850 marriage to his foster sister, Ellen. Later he moved to Louisiana, and, after the state seceded, Sherman returned to the North to fight for the Union. Sherman covers the general’s early Civil War assignments in Kentucky and Missouri and his battles against former Southern friends there, the battle at Shiloh, and his rise to become second only to Grant among the Union leadership. Sherman’s famed use of destructive war, controversial then and now, is examined in detail. The destruction of property, he believed, would convince the Confederates that surrender was their best option, and Sherman’s successful strategy became the stuff of legend. This definitive biography, which includes forty-six illustrations, effectively refutes misconceptions surrounding the controversial Union general and presents Sherman the man, not the myth.
This text focuses on developing an intimate acquaintance with the geometric meaning of curvature and thereby introduces and demonstrates all the main technical tools needed for a more advanced course on Riemannian manifolds. It covers proving the four most fundamental theorems relating curvature and topology: the Gauss-Bonnet Theorem, the Cartan-Hadamard Theorem, Bonnet’s Theorem, and a special case of the Cartan-Ambrose-Hicks Theorem.
Given a degree one normal map and a closed manifold one can form their product. The result is another degree one normal map. In this paper we calculate the surgery obstruction of the product in terms of the obstruction of the original normal map and invariants of the closed manifold provided that the latter is simply connected. The result depends on the congruence class module 4 of the dimension of the closed manifold.
This book is about the smooth classification of a certain class of algebraicsurfaces, namely regular elliptic surfaces of geometric genus one, i.e. elliptic surfaces with b1 = 0 and b2+ = 3. The authors give a complete classification of these surfaces up to diffeomorphism. They achieve this result by partially computing one of Donalson's polynomial invariants. The computation is carried out using techniques from algebraic geometry. In these computations both thebasic facts about the Donaldson invariants and the relationship of the moduli space of ASD connections with the moduli space of stable bundles are assumed known. Some familiarity with the basic facts of the theory of moduliof sheaves and bundles on a surface is also assumed. This work gives a good and fairly comprehensive indication of how the methods of algebraic geometry can be used to compute Donaldson invariants.
Two premier hypnotherapists collaborate on a new edition of this award-winning text, a collection of techniques and information about hypnosis that no serious student or practitioner should be without. A thorough and practical handbook of various hypnotherapeutic measures, it contains illustrative examples and logically argued selection methods to help practitioners choose the ideal method for a needed purpose. Section by section, it breaks out the various methods and phenomena of hypnosis into easily digested chunks, so the reader can pick and choose at leisure. An excellent practical guide and reference that is sure to be used regularly. The authors have a wide and longstanding experience on the subject and thus can stay on clinically approvable methods.
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