Titlebook: Loop Spaces, Characteristic Classes and Geometric Quantization; Jean-Luc Brylinski Textbook 1993 Birkh?user Boston 1993 Algebra.Category t

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2197-1803 inally, the last chapter deals with the Dirac monopole and Dirac’s quantization of the electrical charge...The book will be of interest to topologists, geometers, Lie the978-0-8176-4730-8978-0-8176-4731-5Series ISSN 2197-1803 Series E-ISSN 2197-1811

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Complexes of Sheaves and their Hypercohomology,. Oka [.] and H. Cartan himself), and by J. Leray in topology [.]. Since then sheaves have become important in many other branches of mathematics. Whenever one wants to investigate global properties of geometric objects like functions, bundles, and so on, sheaves come into play. There are many excel

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Line Bundles and Central Extensions,. This group turns out to be isomorphic to a Deligne cohomology group (§2.2). In fact Deligne cohomology provides a tool for constructing line bundles with connections. If the infinitesimal action of some Lie algebra on the underlying manifold preserves the isomorphism class of (., ?), then a centra

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,K?hler Geometry of the Space of Knots,/? and denote by . the parameter in ?/?. First, recall from [P-S] how the space . of smooth loops .. → . is made into a smooth manifold, modelled on the topological vector space ..(..,?.). This vector space has the structure of an ILH space (inverse limit of Hilbert spaces) in the sense of §1.4.

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Degree 3 Cohomology: The Dixmier-Douady Theory, a theorem of Weil and Kostant (Corollary 2.1.4) which asserts that ..(.,?) is the group of isomorphism classes of line bundles over . Moreover, given a line bundle ., the corresponding class ..(.) in .. (.,?) is represented by . · ., where . is the curvature of a connection on . We wish to find a s

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Degree 3 Cohomology: Sheaves of Groupoids,ry of descent for sheaves, based on local homeomorphisms. In §2, we introduce sheaves of groupoids (also called stacks) and gerbes. We relate gerbes on . with band a sheaf of abelian groups . with the cohomology group ..(.). A gerbe with band ..* is called a Dixmier-Douady sheaf of groupoids. In §3

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d elsewhere in this volume. In this chapter we will describe the use of isobaric tags for relative and absolute quantification (iTRAQ). These chemical tags attach to all peptides in a protein digest via free amines at the peptide N-terminus and on the side chain of lysine residues. Labelled samples

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Jean-Luc Brylinski of a given protein sequence can have profound effects on the regulation of protein function. Thus, the identification of sites of post-translational modification is crucial for fully deciphering the biological roles of any given protein. The acute regulation and typically low stoichiometry of many

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