Geometry of Vector Sheaves : An Axiomatic Approach to Differential Geometry (Mathematics and its Applications)

Mallios, Anastasios

Kluwer Academic Publishers（1998/12発売）

• 製本 Hardcover:ハードカバー版／ページ数 462 p.
• 言語 ENG
• 商品コード 9780792350040
• DDC分類 516.362

Full Description

This text is part of a two-volume monograph which obtains fundamental notions and results of the standard differential geometry of smooth manifolds, without using differential calculus. Here, the sheaf-theoretic character is emphasized. This has theoretical advantages such as greater perspective, clarity and unification, but also practical benefits ranging from elementary particle physics, via gauge theories and theoretical cosmology ("differential spaces"), to non-linear PDEs (generalized functions). Thus, more general applications, which are no longer "smooth" in the classical sense, can be coped with. The treatise might also be construed as a new systematic endeavour to confront the ever-increasing notion that the "world around us is far from being smooth enough". This work is intended for postgraduate students and researchers whose work involves differential geometry, global analysis, analysis on manifolds, algebraic topology, sheaf theory, cohomology, functional analysis or abstract harmonic analysis.

Contents

I. Sheaf Theory. II. II. Sheaves and Presheaves with Algebraic Structure. III. Sheaf Cohomology. IV. Linear and Multilinear Algebra of Vector Sheaves. V. Vector Sheaves and Cohomology. Appendix: Category Jargon.