This monograph describes important techniques of stable homotopy theory, bothclassical 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 ina 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 andthereby 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. Introduction of the newupper triangular technology method Detailed application of upper triangular technology to operations in algebraic K-theory and to the Arf-Kervaire invariant problem. An account of the relation of the book’s classical stable homotopy theory results to the important, new motivic stable homotopy theory of Morel-Voevodsky
- ISBN: 978-3-7643-9903-0
- Editorial: Birkhaüser
- Encuadernacion: Cartoné
- Páginas: 250
- Fecha Publicación: 01/02/2009
- Nº Volúmenes: 1
- Idioma: Inglés