{"product_id":"differential-geometry-and-topology-studies-in-advanced-mathematics-9781584882534","title":"Differential Geometry and Topology (Studies in Advanced Mathematics)","description":"\u003cp\u003eAccessible  concise  and self-contained  this book offers an outstanding introduction to three related subjects: differential geometry  differential topology  and dynamical systems. Topics of special interest addressed in the book include Brouwers fixed point theorem  Morse Theory  and the geodesic flow. Smooth manifolds  Riemannian metrics  affine connections  the curvature tensor  differential forms  and integration on manifolds provide the foundation for many applications in dynamical systems and mechanics. The authors also discuss the Gauss-Bonnet theorem and its implications in non-Euclidean geometry models. The differential topology aspect of the book centers on classical  transversality theory  Sards theorem  intersection theory  and fixed-point theorems. The construction of the de Rham cohomology builds further arguments for the strong connection between the differential structure and the topological structure. It also furnishes some of the tools necessary for a complete understanding of the Morse theory. These discussions are followed by an introduction to the theory of hyperbolic systems  with emphasis on the quintessential role of the geodesic flow. The integration of geometric theory  topological theory  and concrete applications to dynamical systems set this book apart. With clean  clear prose and effective examples  the authors intuitive approach creates a treatment that is comprehensible to relative beginners  yet rigorous enough for those with more background and experience in the field.\u003c\/p\u003e","brand":"My Store","offers":[{"title":"Default Title","offer_id":45651962789941,"sku":"ByrdShop_1584882530","price":207.2,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0627\/8139\/0901\/files\/9781584882534.jpg?v=1781847856","url":"https:\/\/atxbooks.com\/products\/differential-geometry-and-topology-studies-in-advanced-mathematics-9781584882534","provider":"ATX Books","version":"1.0","type":"link"}