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Stable Homotopy Around the Arf-Kervaire Invariant
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This monograph describes important techniques of stable homotopy theory, both classical and brand new, applying them to the long-standing unsolved problem of the existence of framed manifolds with odd Arf-Kervaire invariant. Opening with an account of the necessary algebraic topology background, it proceeds in a quasi-historical manner to draw from the author's contributions over several decades. A new technique entitled 'upper triangular technology' is introduced which enables the author to relate Adams operations to Steenrod operations and thereby to recover most of the important classical Arf-Kervaire invariant results quite simply. The final chapter briefly relates the book to the contemporary motivic stable homotopy theory of Morel-Voevodsky. Excerpt from a review: 'This takes the reader on an unusual mathematical journey. The problem referred to in the title, its history and the author's relationship with it are lucidly described in the book. The book does not offer a solution, but a new and interesting way of looking at it.
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376439904X
9783764399030
9783764399047