ISBN: 9781156603116

Purchase includes free access to book updates online and a free trial membership in the publisher's book club where you can select from more than a million books without charge. Chapters:… Plus…

Purchase includes free access to book updates online and a free trial membership in the publisher's book club where you can select from more than a million books without charge. Chapters: Grothendieck Topology, Sheaf, Kripke Semantics, Topos, D-Module, Germ, Stalk, Coherent Sheaf, Sheaf Cohomology, Ringed Space, Injective Sheaf, Coherent Duality, Constant Sheaf, Verdier Duality, Cousin Problems, Borel-moore Homology, Flat Topology, Hyperfunction, Image Functors for Sheaves, Gerbe, Ideal Purchase includes free access to book updates online and a free trial membership in the publisher's book club where you can select from more than a million books without charge. Chapters: Grothendieck Topology, Sheaf, Kripke Semantics, Topos, D-Module, Germ, Stalk, Coherent Sheaf, Sheaf Cohomology, Ringed Space, Injective Sheaf, Coherent Duality, Constant Sheaf, Verdier Duality, Cousin Problems, Borel-moore Homology, Flat Topology, Hyperfunction, Image Functors for Sheaves, Gerbe, Ideal Sheaf, Inverse Image Functor, Locally Constant Function, Exceptional Inverse Image Functor, Exponential Sheaf Sequence, Local Cohomology, Direct Image Functor, Sheaf Extension, Holomorphic Sheaf, Restriction, Invertible Sheaf, Abstract Differential Geometry, Godement Resolution, Leray Spectral Sequence, Local System, Algebraic Analysis, Presheaf, Sheaf Spanned by Global Sections, Leray's Theorem, Locally Free Sheaf, de Rham-weil Theorem, Leray Cover. Excerpt: The adjective abstract has often been applied to differential geometry before, but the abstract differential geometry (ADG) of this article is a form of differential geometry without the calculus notion of smoothness, developed by Anastasios Mallios and others from 1998 onwards. Instead of calculus, an axiomatic treatment of differential geometry is built via sheaf theory and sheaf cohomology using vector sheaves in place of bundles based on arbitrary topological spaces. Mallios says noncommutative geometry can be considered a special case of ADG, and that ADG is similar to synthetic differential geometry. Applications ADG Gravity Mallios and Raptis use ADG to avoid the singularities in general relativity and propose this as a route to quantum gravity. References (URLs online) Further reading See also (online edition) A hyperlinked version of this chapter is at Algebraic analysis is an area of mathematics that deals with systems of linear partial differential equations by using sheaf theory and complex analysis to Books, , Sheaf-Theory~~Books-Llc, 999999999, Sheaf Theory, Books Llc, 1156603110, General Books LLC, , , , , General Books LLC<

ISBN: 9781156603116

Purchase includes free access to book updates online and a free trial membership in the publisher's book club where you can select from more than a million books without charge. Chapters:… Plus…

Purchase includes free access to book updates online and a free trial membership in the publisher's book club where you can select from more than a million books without charge. Chapters: Grothendieck Topology, Sheaf, Kripke Semantics, Topos, D-Module, Germ, Stalk, Coherent Sheaf, Sheaf Cohomology, Ringed Space, Injective Sheaf, Coherent Duality, Constant Sheaf, Verdier Duality, Cousin Problems, Borel-moore Homology, Flat Topology, Hyperfunction, Image Functors for Sheaves, Gerbe, Ideal Purchase includes free access to book updates online and a free trial membership in the publisher's book club where you can select from more than a million books without charge. Chapters: Grothendieck Topology, Sheaf, Kripke Semantics, Topos, D-Module, Germ, Stalk, Coherent Sheaf, Sheaf Cohomology, Ringed Space, Injective Sheaf, Coherent Duality, Constant Sheaf, Verdier Duality, Cousin Problems, Borel-moore Homology, Flat Topology, Hyperfunction, Image Functors for Sheaves, Gerbe, Ideal Sheaf, Inverse Image Functor, Locally Constant Function, Exceptional Inverse Image Functor, Exponential Sheaf Sequence, Local Cohomology, Direct Image Functor, Sheaf Extension, Holomorphic Sheaf, Restriction, Invertible Sheaf, Abstract Differential Geometry, Godement Resolution, Leray Spectral Sequence, Local System, Algebraic Analysis, Presheaf, Sheaf Spanned by Global Sections, Leray's Theorem, Locally Free Sheaf, de Rham-weil Theorem, Leray Cover. Excerpt: The adjective abstract has often been applied to differential geometry before, but the abstract differential geometry (ADG) of this article is a form of differential geometry without the calculus notion of smoothness, developed by Anastasios Mallios and others from 1998 onwards. Instead of calculus, an axiomatic treatment of differential geometry is built via sheaf theory and sheaf cohomology using vector sheaves in place of bundles based on arbitrary topological spaces. Mallios says noncommutative geometry can be considered a special case of ADG, and that ADG is similar to synthetic differential geometry. Applications ADG Gravity Mallios and Raptis use ADG to avoid the singularities in general relativity and propose this as a route to quantum gravity. References (URLs online) Further reading See also (online edition) A hyperlinked version of this chapter is at Algebraic analysis is an area of mathematics that deals with systems of linear partial differential equations by using sheaf theory and complex analysis to Books, , Sheaf-Theory~~Books-Llc, , , , , , , , , , General Books LLC<

2012, ISBN: 1156603110

[EAN: 9781156603116], Libro nuovo, [SC: 0.0], [PU: Books LLC, Wiki Series, United States], Language: English. Brand new Book. Please note that the content of this book primarily consists … Plus…

[EAN: 9781156603116], Libro nuovo, [SC: 0.0], [PU: Books LLC, Wiki Series, United States], Language: English. Brand new Book. Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 42. Chapters: Grothendieck topology, Sheaf, Kripke semantics, Topos, D-module, Germ, Stalk, Coherent sheaf, Sheaf cohomology, Ringed space, Injective sheaf, Coherent duality, Cousin problems, Verdier duality, Constant sheaf, Borel-Moore homology, Hyperfunction, Flat topology, Image functors for sheaves, Gerbe, Ideal sheaf, Inverse image functor, Godement resolution, Exponential sheaf sequence, Exceptional inverse image functor, Locally constant function, Direct image functor, Local cohomology, Sheaf extension, Restriction, Holomorphic sheaf, Leray cover, Invertible sheaf, Abstract differential geometry, Leray spectral sequence, Local system, Direct image with compact support, Algebraic analysis, Presheaf, Sheaf spanned by global sections, Locally free sheaf, Leray's theorem, De Rham-Weil theorem. Excerpt: In mathematics, a sheaf is a tool for systematically tracking locally defined data attached to the open sets of a topological space. The data can be restricted to smaller open sets, and the data assigned to an open set is equivalent to all collections of compatible data assigned to collections of smaller open sets covering the original one. For example, such data can consist of the rings of continuous or smooth real-valued functions defined on each open set. Sheaves are by design quite general and abstract objects, and their correct definition is rather technical. They exist in several varieties such as sheaves of sets or sheaves of rings, depending on the type of data assigned to open sets. There are also maps (or morphisms) from one sheaf to another; sheaves (of a specific type, such as sheaves of abelian groups) with their morphisms on a fixed topological space form a category. On the other hand, to each continuous map there is associated both a direct image functor, taking sheaves and their morphisms on the domain to sheaves.<

2012, ISBN: 1156603110

[EAN: 9781156603116], Libro nuovo, [SC: 0.0], [PU: Books LLC, Wiki Series, United States], Language: English. Brand new Book. Please note that the content of this book primarily consists … Plus…

[EAN: 9781156603116], Libro nuovo, [SC: 0.0], [PU: Books LLC, Wiki Series, United States], Language: English. Brand new Book. Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 42. Chapters: Grothendieck topology, Sheaf, Kripke semantics, Topos, D-module, Germ, Stalk, Coherent sheaf, Sheaf cohomology, Ringed space, Injective sheaf, Coherent duality, Cousin problems, Verdier duality, Constant sheaf, Borel-Moore homology, Hyperfunction, Flat topology, Image functors for sheaves, Gerbe, Ideal sheaf, Inverse image functor, Godement resolution, Exponential sheaf sequence, Exceptional inverse image functor, Locally constant function, Direct image functor, Local cohomology, Sheaf extension, Restriction, Holomorphic sheaf, Leray cover, Invertible sheaf, Abstract differential geometry, Leray spectral sequence, Local system, Direct image with compact support, Algebraic analysis, Presheaf, Sheaf spanned by global sections, Locally free sheaf, Leray's theorem, De Rham-Weil theorem. Excerpt: In mathematics, a sheaf is a tool for systematically tracking locally defined data attached to the open sets of a topological space. The data can be restricted to smaller open sets, and the data assigned to an open set is equivalent to all collections of compatible data assigned to collections of smaller open sets covering the original one. For example, such data can consist of the rings of continuous or smooth real-valued functions defined on each open set. Sheaves are by design quite general and abstract objects, and their correct definition is rather technical. They exist in several varieties such as sheaves of sets or sheaves of rings, depending on the type of data assigned to open sets. There are also maps (or morphisms) from one sheaf to another; sheaves (of a specific type, such as sheaves of abelian groups) with their morphisms on a fixed topological space form a category. On the other hand, to each continuous map there is associated both a direct image functor, taking sheaves and their morphisms on the domain to sheaves.<