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The most important invariant of a topological space is its fundamental group. When this is trivial, the resulting homotopy theory is well researched and familiar. In the general case, however, homotopy theory over nontrivial fundamental groups is much more problematic and far less well understood. Syzygies and Homotopy Theory explores the problem of nonsimply connected homotopy in the first nontrivial cases and presents, for the first time, a systematic rehabilitation of Hilbert's method of syzygies in the context of non-simply connected homotopy theory. The first part of the book is theoretical, formulated to allow a general finitely presented group as a fundamental group. The innovation here is to regard syzygies as stable modules rather than minimal modules. Inevitably this forces a reconsideration of the problems of noncancellation; these are confronted in the second, practical, part of the book. In particular, the second part of the book considers how the theory works out in detail for the specific examples Fn ´F where Fn is a free group of rank n and F is finite. Another innovation is to parametrize the first syzygy in terms of the more familiar class of stably free modules. Furthermore, detailed description of these stably free modules is effected by a suitable modification of the method of Milnor squares. The theory developed within this book has potential applications in various branches of algebra, including homological algebra, ring theory and K-theory. Syzygies and Homotopy Theory will be of interest to researchers and also to graduate students with a background in algebra and algebraic topology.

Homotopy theory. --- Syzygies (Mathematics). --- Homotopy theory --- Syzygies (Mathematics) --- Mathematics --- Physical Sciences & Mathematics --- Geometry --- Algebra --- Algebraic topology. --- Algebra. --- Deformations, Continuous --- Syzygy theory (Mathematics) --- Mathematics. --- Commutative algebra. --- Commutative rings. --- Group theory. --- Group Theory and Generalizations. --- Commutative Rings and Algebras. --- Mathematical analysis --- Topology --- Categories (Mathematics) --- Rings (Algebra) --- Groups, Theory of --- Substitutions (Mathematics)

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The 5th Battalion of the Royal Irish Fusiliers formed part of the 10th (Irish) Division raised at the outbreak of the Great War in response to Kitchener's call for volunteers. This very concise history relates the battalion's exploits which began at Gallipoli in July 1915. After a hard mauling in this doomed campaign, the battalion recuperated on the Greek island of Lemnos before being hurled into yet another forlorn enterprisxe : the attempt to save Serbia from being overrun. The unit's t...

Great Britain. -- Army. -- Princess Victoria's Royal Irish Fusiliers. -- Battalion, 5th -- History. --- Great Britain. Machine Gun Corps. --- World War, 1914-1918 -- Regimental histories -- Great Britain.

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This second edition of Measuring Nonuse Damages Using Conjoint Valuation is essentially a reprint of a 1992 monograph that has been in steady demand since its original appearance. The RTI Press edition, which is intended to meet continued inquiries and requests for the monograph, contains a Foreword and a Preface to the second edition that put the original work into historical perspective. These studies of ways to value stated preferences, as applied then to the Exxon Valdez oil spill, continue to be a timely and still-rigorous examination of such methods; even with the passage of time and statistical advances from the past two decades, the conclusions and insights as to whether and how these techniques might still be employed in valuing use or nonuse losses from similar events remain valid.