John Oprea - Böcker

Rational homotopy is a very powerful tool for differential topology and geometry. This text aims to provide graduates and researchers with the tools necessary for the use of rational homotopy in geometry. Algebraic Models in Geometry has been written for topologists who are drawn to geometrical problems amenable to topological methods and also for geometers who are faced with problems requiring topological approaches and thus need a simple and concrete introduction to rational homotopy. This is essentially a book of applications. Geodesics, curvature, embeddings of manifolds, blow-ups, complex and Kähler manifolds, symplectic geometry, torus actions, configurations and arrangements are all covered. The chapters related to these subjects act as an introduction to the topic, a survey, and a guide to the literature. But no matter what the particular subject is, the central theme of the book persists; namely, there is a beautiful connection between geometry and rational homotopy which both serves to solve geometric problems and spur the development of topological methods.

Rational homotopy is a very powerful tool for differential topology and geometry. This text aims to provide graduates and researchers with the tools necessary for the use of rational homotopy in geometry. Algebraic Models in Geometry has been written for topologists who are drawn to geometrical problems amenable to topological methods and also for geometers who are faced with problems requiring topological approaches and thus need a simple and concrete introduction to rational homotopy. This is essentially a book of applications. Geodesics, curvature, embeddings of manifolds, blow-ups, complex and Kähler manifolds, symplectic geometry, torus actions, configurations and arrangements are all covered. The chapters related to these subjects act as an introduction to the topic, a survey, and a guide to the literature. But no matter what the particular subject is, the central theme of the book persists; namely, there is a beautiful connection between geometry and rational homotopy which both serves to solve geometric problems and spur the development of topological methods.

Differential Geometry and Its Applications studies the differential geometry of surfaces with the goal of helping students make the transition from the compartmentalized courses in a standard university curriculum to a type of mathematics that is a unified whole. It mixes geometry, calculus, linear algebra, differential equations, complex variables, the calculus of variations, and notions from the sciences. That mix of ideas offers students the opportunity to visualize concepts through the use of computer algebra systems such as Maple.Differential Geometry and Its Applications emphasizes that this visualization goes hand in hand with understanding the mathematics behind the computer construction. The book is rich in results and exercises that form a continuous spectrum, from those that depend on calculation to proofs that are quite abstract.