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Starting At An Introductory Level, The Book Leads Rapidly To Important And Often New Results In Synthetic Differential Geometry. From Rudimentary Analysis The Book Moves To Such Important Results As: A New Proof Of De Rham'S Theorem; The Synthetic View Of Global Action, Going As Far As The Weil Characteristic Homomorphism; The Systematic Account Of Structured Lie Objects, Such As Riemannian, Symplectic, Or Poisson Lie Objects; The View Of Global Lie Algebras As Lie Algebras Of A Lie Group In The Synthetic Sense; And Lastly The Synthetic Construction Of Symplectic Structure On The Cotangent Bundle In General. Thus While The Book Is Limited To A Naive Point Of View Developing Synthetic Differential Geometry As A Theory In Itself, The Author Nevertheless Treats Somewhat Advanced Topics, Which Are Classic In Classical Differential Geometry But New In The Synthetic Context.Audience: The Book Is Suitable As An Introduction To Synthetic Differential Geometry For Students As Well As More Qualified Mathematicians.
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