Let [italic capital]G be a compact Lie group, [italic capitals]EG a contractible free [italic capital]G-space and let [italic capitals]E~G be the unreduced suspension of [italic capitals]EG with one of the cone points as basepoint. Let [italic]k*[over][subscript italic capital]G be a [italic capital]G-spectrum. Let [italic capital]X+ denote the disjoint union of [italic capital]X and a [italic capital]G-fixed basepoint. Define the [italic capital]G-spectra [italic]f([italic]k*[over][subscript italic capital]G) = [italic]k*[over][subscript italic capital]G [up arrowhead symbol] [italic capitals]EG+, [italic]c([italic]k*[over][subscript italic capital]G) = [italic capital]F([italic capitals]EG+,[italic]k*[over][subscript italic capital]G), and [italic]t([italic]k[subscript italic capital]G)* = [italic capital]F([italic capitals]EG+,[italic]k*[over][subscript italic capital]G) [up arrowhead symbol] [italic capitals]E~G. The last of these is the [italic capital]G-spectrum representing the generalized Tate homology and cohomology theories associated to [italic]k[subscript italic capital]G. Here [italic capital]F([italic capitals]EG+,[italic]k*[over][subscript italic capital]G) is the function space spectrum. The authors develop the properties of these theories, illustrating the manner in which they generalize the classical Tate-Swan theories.
The theory of elliptic curves involves a blend of algebra, geometry, analysis, and number theory. This book stresses this interplay as it develops the basic theory, providing an opportunity for readers to appreciate the unity of modern mathematics. The book’s accessibility, the informal writing style, and a wealth of exercises make it an ideal introduction for those interested in learning about Diophantine equations and arithmetic geometry.
Beginning with the death of William Shakespeare in 1616, a study of the bard explores his evolution from provincial playwright to universally acclaimed, literary giant, beginning with his growing popularity during the late-seventeenth-century Restoration and ranging to the Stratford celebration of the tricentennial of Shakespeare's birth in 1864.
This book is a one-stop reference resource for the vast variety of musical expressions of the First Peoples' cultures of North America, both past and present. Encyclopedia of Native American Music of North America documents the surprisingly varied musical practices among North America's First Peoples, both historically and in the modern context. It supplies a detailed yet accessible and approachable overview of the substantial contributions and influence of First Peoples that can be appreciated by both native and nonnative audiences, regardless of their familiarity with musical theory. The entries address how ethnomusicologists with Native American heritage are revolutionizing approaches to the discipline, and showcase how musicians with First Peoples' heritage are influencing modern musical forms including native flute, orchestral string playing, gospel, and hip hop. The work represents a much-needed academic study of First Peoples' musical cultures—a subject that is of growing interest to Native Americans as well as nonnative students and readers.
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