Virtual Topology and Functor Geometry: Lecture Notes in Pure and Applied Mathematics
Autor Fred Van Oystaeyenen Limba Engleză Paperback – 15 noi 2007
Presenting the material in an easy, colloquial style to facilitate understanding, the book begins with an introduction to category theory, followed by a chapter on noncommutative spaces. This chapter examines noncommutative lattices, noncommutative opens, sheaf theory, the generalized Stone space, and Grothendieck topology. The author then studies Grothendieck categorical representations to formulate an abstract notion of "affine open". The final chapter proposes a dynamical version of topology and sheaf theory, providing at least one solution of the problem of sheafification independent of generalizations of topos theory.
By presenting new ideas for the development of an intrinsically noncommutative geometry, this book fosters the further unification of different kinds of noncommutative geometry and the expression of observations that involve natural phenomena.
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Specificații
ISBN-13: 9781420060560
ISBN-10: 1420060562
Pagini: 168
Ilustrații: 51 Illustrations, black and white
Dimensiuni: 156 x 234 x 11 mm
Greutate: 0.29 kg
Ediția:1
Editura: CRC Press
Colecția Chapman and Hall/CRC
Seria Lecture Notes in Pure and Applied Mathematics
ISBN-10: 1420060562
Pagini: 168
Ilustrații: 51 Illustrations, black and white
Dimensiuni: 156 x 234 x 11 mm
Greutate: 0.29 kg
Ediția:1
Editura: CRC Press
Colecția Chapman and Hall/CRC
Seria Lecture Notes in Pure and Applied Mathematics
Public țintă
ProfessionalCuprins
Foreword. Introduction. Projects. A Taste of Category Theory. Noncommutative Spaces. Grothendieck Categorical Representations. Sheaves and Dynamical Topology. Bibliography. Index.
Recenzii
"This book has a special character. Its main theme is to describe development of new branches of non-commutative geometry on a different level of realizations, ranging from areas already fully developed to many different suggestions for possible future investigations. … the book is very inspiring and worth reading."
—EMS Newsletter, December 2009
—EMS Newsletter, December 2009
Descriere
This work explores new aspects of virtual topology and functor geometry as well as more established facets of noncommutative algebra. The author suggests possible projects that range from straightforward exercises to advanced research level and supplies the necessary background material, including localization theory and the classical lattice of quantum mechanics for a Hilbert space. Presenting the material in an easy, colloquial style to facilitate understanding, he covers category theory and noncommutative spaces, formulates an abstract notion of "affine open" through Grothendieck categorical representations, and proposes a dynamical version of topology and sheaf theory.