Sheaf Theory: Graduate Texts in Mathematics -Glen E. Bredon Education Book

Description: FAST SHIPPING HASSLE FREE RETURNS SECURE PAYMENT EXCELLENT SERVICE Sheaf Theory: Graduate Texts in MathematicsAuthor: Glen E. BredonPublisher: SpringerCategory: Mathematics, Algebra, Geometry, Topology, Algebraic TopologyBook Format: Hardcover Shipping Please make sure to double check your shipping and address information before you confirm and pay. Where do you ship? Currently, we ship online purchases Australia wide. How long till my item gets dispatched? In most cases, orders made before 2 PM will be dispatched same day or within 24 hours. In some cases, handling time may take longer. If this is the case, specific handling time will be displayed explicitly in the listing. How long until I get my order? Unless you live in a remote area, most orders will be delivered within 2-5 business days at your destination, remote areas may take a little bit longer. Who are my items shipped with? 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The item must still be in its original condition and packaging.In these cases the customer will be responsible to pay the return postage. DESCRIPTION Sheaf Theory: Graduate Texts in MathematicsAuthor: Glen E. BredonPublisher: SpringerCategory: Mathematics, Algebra, Geometry, Topology, Algebraic TopologyBook Format: Hardcover This book is primarily concerned with the study of cohomology theories of general topological spaces with general coefficient systems. The parts of sheaf theory covered here are those areas important to algebraic topology. There are several innovations in this book. The concept of the tautness of a subspace is introduced and exploited throughout the book. The fact that sheaf theoretic cohomology satisfies the homotopy property is proved for general topological spaces. Relative cohomology is introduced into sheaf theory. The reader should have a thorough background in elementary homological algebra and in algebraic topology. A list of exercises at the end of each chapter will help the student to learn the material, and solutions of many of the exercises are given in an appendix. The new edition of this classic in the field has been substantially rewritten with the addition of over 80 examples and of further explanatory material. Among the items added are new sections on Cech cohomology, the Oliver transfer, intersection theory, generalized manifolds, locally homogeneous spaces, homological fibrations and Table Of ContentsI Sheaves and Presheaves.- Definitions.- 2 Homomorphisms, subsheaves, and quotient sheaves.- 3 Direct and inverse images.- 4 Cohomomorphisms.- 5 Algebraic constructions.- 6 Supports.- 7 Classical cohomology theories.- Exercises.- II Sheaf Cohomology.- 1 Differential sheaves and resolutions.- 2 The canonical resolution and sheaf cohomology.- 3 Injective sheaves.- 4 Acyclic sheaves.- 5 Flabby sheaves.- 6 Connected sequences of functors.- 7 Axioms for cohomology and the cup product.- 8 Maps of spaces.- 9 ?-soft and ?-fine sheaves.- 10 Subspaces.- 11 The Vietoris mapping theorem and homotopy invariance.- 12 Relative cohomology.- 13 Mayer-Vietoris theorems.- 14 Continuity.- 15 The Kunneth and universal coefficient theorems.- 16 Dimension.- 17 Local connectivity.- 18 Change of supports; local cohomology groups.- 19 The transfer homomorphism and the Smith sequences.- 20 Steenrod's cyclic reduced powers.- 21 The Steenrod operations.- Exercises.- III Comparison with Other Cohomology Theories.- 1 Singular cohomology.- 2 Alexander-Spanier cohomology.- 3 de Rham cohomology.- 4 ?ech cohomology.- Exercises.- IV Applications of Spectral Sequences.- 1 The spectral sequence of a differential sheaf.- 2 The fundamental theorems of sheaves.- 3 Direct image relative to a support family.- 4 The Leray sheaf.- 5 Extension of a support family by a family on the base space.- 6 The Leray spectral sequence of a map.- 7 Fiber bundles.- 8 Dimension.- 9 The spectral sequences of Borel and Cartan.- 10 Characteristic classes.- 11 The spectral sequence of a filtered differential sheaf.- 12 The Fary spectral sequence.- 13 Sphere bundles with singularities.- 14 The Oliver transfer and the Conner conjecture.- Exercises.- V Borel-Moore Homology.- 1 Cosheaves.- 2 The dual of a differential cosheaf.- 3 Homology theory.- 4 Maps of spaces.- 5 Subspaces and relative homology.- 6 The Vietoris theorem, homotopy, and covering spaces.- 7 The homology sheaf of a map.- 8 The basic spectral sequences.- 9 Poincare duality.- 10 The cap product.- 11 Intersection theory.- 12 Uniqueness theorems.- 31 Uniqueness theorems for maps and relative homology.- 14 The Kunneth formula.- 15 Change of rings.- 16 Generalized manifolds.- 17 Locally homogeneous spaces.- 18 Homological fibrations and p-adic transformation groups.- 19 The transfer homomorphism in homology.- 20 Smith theory in homology.- Exercises.- VI Cosheaves and ?ech Homology.- 1 Theory of cosheaves.- 2 Local triviality.- 3 Local isomorphisms.- 4 Cech homology.- 5 The reflector.- 6 Spectral sequences.- 7 Coresolutions.- 8 Relative ?ech homology.- 9 Locally paracompact spaces.- 10 Borel-Moore homology.- 11 Modified Borel-Moore homology.- 12 Singular homology.- 13 Acyclic coverings.- 14 Applications to maps.- Exercises.- A Spectral Sequences.- 1 The spectral sequence of a filtered complex.- 2 Double complexes.- 3 Products.- 4 Homomorphisms.- B Solutions to Selected Exercises.- Solutions for Chapter I.- Solutions for Chapter II.- Solutions for Chapter III.- Solutions for Chapter IV.- Solutions for Chapter V.- Solutions for Chapter VI.- List of Symbols.- List of Selected Facts. 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As long as the item is still in factory sealed new condition it may be sent back to us within 30 days of purchase. The item must still be in its original condition and packaging.In these cases the customer will be responsible to pay the return postage. CONTACT More Questions? If there is any problem, please contact us. We would rather issue a refund or a replacement item than have an unhappy customer. Our customers come first and we would love to hear from you. Feel free to CONTACT US at any time with any questions or concerns and we will be more than glad to assist you. Copyright © | All Rights Reserved

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