Configuration spaces : geometry, topology and representation theory /: geometry, topology and representation theory. ([2016])

• Record Type: Book
• Further Information: Note: Filippo Callegaro, Frederick Cohen, Corrado De Concini, Eva Maria Feichtner, Giovanni Gaiffi, Mario Salvetti, editors.
• Editors: Callegaro, Filippo; Cohen, Frederick; De Concini, Corrado; Feichtner, Eva Maria; Gaiffi, Giovanni; Salvetti, Mario
• Contents: Preface; Contents; Contributors; About the Editors; Around the Tangent Cone Theorem; 1 Introduction; 1.1 Resonance Varieties; 1.2 Characteristic Varieties; 1.3 Quasi-Projective Varieties; 2 The Resonance Varieties of a cdga; 2.1 Commutative Differential Graded Algebras; 2.2 Resonance Varieties; 2.3 A Generalized Koszul Complex; 2.4 Alternate Views of Resonance; 3 The Resonance Varieties of a Space; 3.1 The Cohomology Algebra; 3.2 The Sullivan Model; 3.3 An Algebraic Tangent Cone Theorem; 3.4 Positive Weights; 4 Characteristic Varieties; 4.1 Homology Jump Loci for Rank 1 Local Systems. 4.2 Some Properties of the Characteristic Varieties4.3 Alexander Varieties; 5 The Tangent Cone Theorem; 5.1 Two Types of Tangent Cones; 5.2 Germs of Jump Loci; 5.3 Tangent Cones and Jump Loci; 5.4 The Influence of Formality; 5.5 Formality Tests; 6 Smooth Quasi-Projective Varieties; 6.1 Compactifications and Formality; 6.2 Algebraic Models; 6.3 Configuration Spaces; 6.4 Characteristic Varieties; 6.5 Resonance Varieties; 6.6 Resonance in Degree 1; 7 Hyperplane Arrangements and the Milnor Fibration; 7.1 Complement and Intersection Lattice; 7.2 Cohomology Jump Loci of the Complement. 7.3 The Milnor Fibration7.4 Cohomology Jump Loci of the Milnor Fiber; 7.5 Formality of the Milnor Fiber; 8 Elliptic Arrangements; 8.1 Complements of Elliptic Arrangements; 8.2 An Algebraic Model; 8.3 Ordered Configurations on an Elliptic Curve; References; Higher Resonance Varieties of Matroids; 1 Introduction; 1.1 Outline; 2 Background; 2.1 Arrangements and Matroids; 2.2 Projectivization; 2.3 A Category of Matroids; 3 Resonance Varieties; 3.1 Definitions; 3.2 Resonance of Orlik-Solomon Algebras; 3.3 Top and Bottom; 3.4 Upper Bounds; 4 Matroid Operations and Resonance; 4.1 Naturality. 4.2 Sums, Submatroids and Duals4.3 Local Components; 4.4 Deletion-Contraction; 4.5 Parallel Connections; 5 Singular Subspaces and Multinets; 5.1 R1(M): Multinets; 5.2 R>1(M): Singular Subspaces; References; Local Asymptotic Euler-Maclaurin Expansion for Riemann Sums over a Semi-Rational Polyhedron; 1 Introduction; 2 Notations and Basic Facts; 2.1 Various Notations; 2.1.1 Vector Spaces; 2.1.2 Bernoulli Numbers and Polynomials; 2.1.3 Fractional Part of a Real Number; 2.1.4 Fourier Transform; 2.2 Polyhedra, Cones; 2.2.1 Convex Polyhedron; 2.2.2 Subdivision of a Cone into Unimodular Ones. 2.3 Discrete and Continuous Generating Functions of a Pointed Polyhedron S(p), I(p)3 Asymptotic Expansions for Riemann Sums over a Cone ; 3.1 Dimension One; 3.2 Fourier Transforms and Boundary Values; 3.3 Asymptotic Expansion of the Fourier Transform of a Riemann Sum over a Cone; 3.4 Asymptotic Expansions of Riemann Sums over Cones in Terms of Differential Operators; 4 Simplicial Cones and Normal Derivatives Formula; 4.1 Asymptotic Expansions of Riemann Sums and Todd Operator; 4.2 Local Euler-Maclaurin Formula.
• Publisher Details: Switzerland : Springer
• Publication Date: 2016
• Extent: 1 online resource
• Subjects: 514; Mathematics; Topology; MATHEMATICS -- Topology; Topology; Mathematics -- Combinatorics; Mathematics -- Geometry -- Algebraic; Topology; Combinatorics & graph theory; Algebraic geometry; Geometry; Combinatorics; Geometry, algebraic; Mathematics -- Geometry -- General; Geometry; Electronic books
• Languages: English
• ISBNs: 9783319315805; 3319315803
• Related ISBNs: 9783319315799; 331931579X
• Notes: Note: Includes bibliographical references.; Note: Vendor-supplied metadata.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.