Ivancevic_Applied-Diff-Geom

Glossary of Frequently Used Symbolsxvbase point as morphisms;V – all vector spaces as objects and all linear maps between them as morphisms;B – Banach spaces over R as objects and bounded linear maps betweenthem as morphisms;G – all groups as objects, all homomorphisms between them as morphisms;A – Abelian groups as objects, homomorphisms between them as morphisms;AL – all algebras (over a given number field K) as objects, all their homomorphismsbetween them as morphisms;T – all topological spaces as objects, all continuous functions between themas morphisms;PT – pointed topological spaces as objects, continuous functions betweenthem preserving base point as morphisms;T G – all topological groups as objects, their continuous homomorphisms asmorphisms;M – all smooth manifolds as objects, all smooth maps between them asmorphisms;M n – nD manifolds as objects, their local diffeomorphisms as morphisms;LG – all Lie groups as objects, all smooth homomorphisms between themas morphisms;LAL – all Lie algebras (over a given field K) as objects, all smooth homomorphismsbetween them as morphisms;T B – all tangent bundles as objects, all smooth tangent maps between themas morphisms;T ∗ B – all cotangent bundles as objects, all smooth cotangent maps betweenthem as morphisms;VB – all smooth vector bundles as objects, all smooth homomorphisms betweenthem as morphisms;FB – all smooth fibre bundles as objects, all smooth homomorphisms betweenthem as morphisms;Symplec – all symplectic manifolds (i.e., physical phase–spaces), all symplecticmaps (i.e., canonical transformations) between them as morphisms;Hilbert – all Hilbert spaces and all unitary operators as morphisms.