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Differential Geometry in the Large
From Ricci flow to GIT, physics to curvature bounds, Sasaki geometry to almost formality. This is differential geometry at large.
The Disc Embedding Theorem
The Disc Embedding Theorem contains the first thorough and approachable exposition of Freedman's proof of the disc embedding theorem.
Introduction to Mathematics
This textbook is designed for an Introduction to Proofs course organized around the themes of number and space. Concepts are illustrated using both geometric and number examples, while frequent analogies and applications help build intuition and context in the humanities, arts, and sciences. Sophisticated mathematical ideas are introduced early and then revisited several times in a spiral structure, allowing students to progressively develop rigorous thinking. Throughout, the presentation is enlivened with whimsical illustrations, apt quotations, and glimpses of mathematical history and culture. Early chapters integrate an introduction to sets, logic, and beginning proof techniques with a fi...
I Die in a Good Cause –
Originally from west Kerry, Thomas Ashe was a schoolteacher in north County Dublin and a founding member of the Irish Volunteers. During the 1916 Rising he commanded the Fingal Battalion of the Volunteers, who were tasked with destroying the communications network of the British establishment north of Dublin city. This culminated in the Battle of Ashbourne, where the tactics used were a precursor of the guerrilla warfare techniques that were to be so effective in the War of Independence. Ashe was sentenced to death alongside Éamon de Valera, but their sentences were commuted to life imprisonment. He led a hunger strike in Lewes Prison in May 1917 and was released under a general amnesty in June. Ashe was re-arrested in August for a speech he made in Co. Longford. He was imprisoned in Mountjoy, where he went on hunger strike in September for prisoner-of-war status. He died on 25 September, having been force-fed by the prison authorities. Michael Collins delivered the oration at his funeral and the circumstances of his death and funeral became one of the key factors in tipping public opinion towards supporting the cause of the 1916 rebels.
Discourse on a New Method
Addressing a wide range of topics, from Newton to Post-Kuhnian philosophy of science, these essays critically examine themes that have been central to the influential work of philosopher Michael Friedman. Special focus is given to Friedman's revealing study of both history of science and philosophy in his work on Kant, Newton, Einstein, and other major figures. This interaction of history and philosophy is the subject of the editors' "manifesto" and serves to both explain and promote the essential ties between two disciplines usually regarded as unrelated.
Quantum Chance and Non-locality
The book will appeal to anyone with an interest in the interpretation of quantum mechanics.
Algebraic and Geometric Surgery
This book is an introduction to surgery theory: the standard classification method for high-dimensional manifolds. It is aimed at graduate students who have already had a basic topology course, and would now like to understand the topology of high-dimensional manifolds. This text contains entry-level accounts of the various prerequisites of both algebra and topology, including basic homotopy and homology, Poincare duality, bundles, cobordism, embeddings, immersions, Whitehead torsion, Poincare complexes, spherical fibrations and quadratic forms and formations. While concentrating on the basic mechanics of surgery, this book includes many worked examples, useful drawings for illustration of the algebra and references for further reading.
The Novikov Conjecture
These lecture notes contain a guided tour to the Novikov Conjecture and related conjectures due to Baum-Connes, Borel and Farrell-Jones. They begin with basics about higher signatures, Whitehead torsion and the s-Cobordism Theorem. Then an introduction to surgery theory and a version of the assembly map is presented. Using the solution of the Novikov conjecture for special groups some applications to the classification of low dimensional manifolds are given.
Complex Analysis
All needed notions are developed within the book: with the exception of fundamentals which are presented in introductory lectures, no other knowledge is assumed Provides a more in-depth introduction to the subject than other existing books in this area Over 400 exercises including hints for solutions are included
Noncommutative Localization in Algebra and Topology
Noncommutative localization is a powerful algebraic technique for constructing new rings by inverting elements, matrices and more generally morphisms of modules. Originally conceived by algebraists (notably P. M. Cohn), it is now an important tool not only in pure algebra but also in the topology of non-simply-connected spaces, algebraic geometry and noncommutative geometry. This volume consists of 9 articles on noncommutative localization in algebra and topology by J. A. Beachy, P. M. Cohn, W. G. Dwyer, P. A. Linnell, A. Neeman, A. A. Ranicki, H. Reich, D. Sheiham and Z. Skoda. The articles include basic definitions, surveys, historical background and applications, as well as presenting new results. The book is an introduction to the subject, an account of the state of the art, and also provides many references for further material. It is suitable for graduate students and more advanced researchers in both algebra and topology.
