Calculus to cohomology : De Rham cohomology and characteristic classes
Madsen, Ib H.
Calculus to cohomology : De Rham cohomology and characteristic classes - 1st ed. - Cambridge: Cambridge University Press, C1997. - vii, 286p. : ill. ; 24cm
Includes appendices, bibliographic references and subject index.
De Rham cohomology is the cohomology of differential forms. This book offers a self-contained exposition to this subject and to the theory of characteristic classes from the curvature point of view. It requires no prior knowledge of the concepts of algebraic topology or cohomology. The first ten chapters study cohomology of open sets in Euclidean space, treat smooth manifolds and their cohomology and end with integration on manifolds. The last eleven chapters include Morse theory, index of vector fields, Poincaré duality, vector bundles, connections and curvature, and the book ends with the general Gauss-Bonnet theorem. The text includes well over 150 exercises, and gives the background to the modern developments in gauge theory and geometry in four dimensions, but it also serves as an introductory course in algebraic topology. It will be invaluable to anyone studying cohomology, curvature, and their applications.
*Only decent treatment of subject at this level
*Thoroughly class tested text with loads of exercises
9780521589567 (pbk.) £ 44.99 = Mathematics
Mathematics
Topology
Cohomology theories
514.23 / MAD
Calculus to cohomology : De Rham cohomology and characteristic classes - 1st ed. - Cambridge: Cambridge University Press, C1997. - vii, 286p. : ill. ; 24cm
Includes appendices, bibliographic references and subject index.
De Rham cohomology is the cohomology of differential forms. This book offers a self-contained exposition to this subject and to the theory of characteristic classes from the curvature point of view. It requires no prior knowledge of the concepts of algebraic topology or cohomology. The first ten chapters study cohomology of open sets in Euclidean space, treat smooth manifolds and their cohomology and end with integration on manifolds. The last eleven chapters include Morse theory, index of vector fields, Poincaré duality, vector bundles, connections and curvature, and the book ends with the general Gauss-Bonnet theorem. The text includes well over 150 exercises, and gives the background to the modern developments in gauge theory and geometry in four dimensions, but it also serves as an introductory course in algebraic topology. It will be invaluable to anyone studying cohomology, curvature, and their applications.
*Only decent treatment of subject at this level
*Thoroughly class tested text with loads of exercises
9780521589567 (pbk.) £ 44.99 = Mathematics
Mathematics
Topology
Cohomology theories
514.23 / MAD
