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By the same reasoningas in the real case, GL(n,C)is a manifold of dimension 2n2 Loring W. Tu Department of Mathematics Tufts University Medford, MA @ c Springer Science + Business Media, LLC This book has been conceived as the first volume of a tetralogy on geometry and topology. I hope that Volume 3, Differential Geometry: Connections, Curvature, and Characteristic Classes, will soon see the light of day. Introduction to Smooth Manifolds. Sch. of Math., Nagoya Univ Thecomplex general linear groupGL(n,C)is defined to be the group of non singularn×ncomplex matrices. this will be a book to introduce and prepare you in differential geometry, enjoy and practice it An introduction to manifolds. An introduction to manifolds. John M. Lee. TL;DR: In this paper, a review of topology, linear algebra, algebraic geometry, and differential equations is presented, along with Loring W. Tu auth. Table of contents ( Review: Raoul Bott and Loring W. Tu, Differential forms in algebraic topology Semantic Scholar. complexmatrices. Corpus ID: WelcomeGrad. × Close Log In. Log in withDownload Free PDF. Loring W. Tu auth. Search within this book. The second volume is Differential Forms in Algebraic Topology cited above. DOI: /SX. Loring W. Tu auth §DifferentialFormsThe Differential of a FunctionLocal Expression for a DifferentialFormThe Cotangent Bundle Loring W. Tu. Part of the book series: Graduate Texts in Mathematics (GTM, volume)k AccessesCitationsAltmetric. Since ann×nmatrixAis nonsingular if and only if detA6=0, GL(n,C)is an open subset of Cn×n≃R2n2, the vector space ofn×n. Volume 4, Elements of Equiv- (GTM) Loring W. Tu-Differential Geometry_ Connections, Curvature, And Characteristic Classes-Springer ()Free ebook download as PDF File.pdf), Text File.txt) or read book online for free.