03758nam a22005775i 4500 978-3-658-10633-1 DE-He213 20210618090448.0 cr nn 008mamaa 160725s2016 gw | s |||| 0|eng d 9783658106331 978-3-658-10633-1 10.1007/978-3-658-10633-1 doi QA169 PBC bicssc MAT002010 bisacsh PBC thema PBF thema 512.6 23 Wedhorn, Torsten. author. aut http://id.loc.gov/vocabulary/relators/aut Manifolds, Sheaves, and Cohomology [electronic resource] / by Torsten Wedhorn. 1st ed. 2016. Wiesbaden : Springer Fachmedien Wiesbaden : Imprint: Springer Spektrum, 2016. XVI, 354 p. 9 illus. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Springer Studium Mathematik - Master, 2509-9310 Topological Preliminaries -- Algebraic Topological Preliminaries -- Sheaves -- Manifolds -- Local Theory of Manifolds -- Lie Groups -- Torsors and Non-abelian Cech Cohomology -- Bundles -- Soft Sheaves -- Cohomology of Complexes of Sheaves -- Cohomology of Sheaves of Locally Constant Functions -- Appendix: Basic Topology, The Language of Categories, Basic Algebra, Homological Algebra, Local Analysis. This book explains techniques that are essential in almost all branches of modern geometry such as algebraic geometry, complex geometry, or non-archimedian geometry. It uses the most accessible case, real and complex manifolds, as a model. The author especially emphasizes the difference between local and global questions. Cohomology theory of sheaves is introduced and its usage is illustrated by many examples. Content Topological Preliminaries - Algebraic Topological Preliminaries - Sheaves - Manifolds - Local Theory of Manifolds - Lie Groups - Torsors and Non-abelian Cech Cohomology - Bundles - Soft Sheaves - Cohomology of Complexes of Sheaves - Cohomology of Sheaves of Locally Constant Functions - Appendix: Basic Topology, The Language of Categories, Basic Algebra, Homological Algebra, Local Analysis Readership Graduate Students in Mathematics / Master of Science in Mathematics About the Author Prof. Dr. Torsten Wedhorn, Department of Mathematics, Technische Universität Darmstadt, Germany. Category theory (Mathematics). Homological algebra. Topological groups. Lie groups. Differential geometry. Global analysis (Mathematics). Manifolds (Mathematics). Category Theory, Homological Algebra. https://scigraph.springernature.com/ontologies/product-market-codes/M11035 Topological Groups, Lie Groups. https://scigraph.springernature.com/ontologies/product-market-codes/M11132 Differential Geometry. https://scigraph.springernature.com/ontologies/product-market-codes/M21022 Global Analysis and Analysis on Manifolds. https://scigraph.springernature.com/ontologies/product-market-codes/M12082 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783658106324 Printed edition: 9783658106348 Springer Studium Mathematik - Master, 2509-9310 https://doi.org/10.1007/978-3-658-10633-1 ZDB-2-SMA ZDB-2-SXMS Mathematics and Statistics (SpringerNature-11649) Mathematics and Statistics (R0) (SpringerNature-43713)