Intersection Spaces, Spatial Homology Truncation, and String Theory

1. Auflage. 2010
ISBN: 978-3-642-12588-1
Verlag: Springer

Buch, Englisch, Band 1997, 224 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 760 g

Reihe: Lecture Notes in Mathematics

Intersection cohomology assigns groups which satisfy a generalized form of Poincaré duality over the rationals to a stratified singular space. This monograph introduces a method that assigns to certain classes of stratified spaces cell complexes, called intersection spaces, whose
ordinary rational homology satisfies generalized Poincaré duality. The cornerstone of the method is a process of spatial homology truncation, whose functoriality properties are analyzed in detail. The material on truncation is autonomous and may be of independent interest tohomotopy theorists. The cohomology of intersection spaces is not isomorphic to intersection cohomology and possesses algebraic features such as perversity-internal cup-products and cohomology operations that are not generally available for intersection cohomology. A mirror-symmetric interpretation, as well as applications to string theory concerning massless D-branes arising in type IIB theory during a Calabi-Yau conifold transition, are discussed.

Zielgruppe

Research

Autoren/Hrsg.

Banagl, Markus

Fachgebiete

• Naturwissenschaften Physik Quantenphysik
• Naturwissenschaften Biowissenschaften Angewandte Biologie Biomathematik
• Naturwissenschaften Physik Physik Allgemein Experimentalphysik
• Mathematik | Informatik Mathematik Topologie Algebraische Topologie
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik Mathematik Geometrie Elementare Geometrie: Allgemeines
• Naturwissenschaften Physik Physik Allgemein Geschichte der Physik

Inhaltsverzeichnis

Iterated Truncation; 1.7 Localization at Odd Primes; 1.8 Summary; 1.9 The Interleaf Category; 1.10 Continuity; Properties of Homology Truncation; 1.11 Fiberwise Homology Truncation; 1.12 Remarks on Perverse Links and Basic Sets Spaces; 2.1 Reflective Algebra; 2.2 The Intersection Space in the Isolated Singularities Case; 2.3 Independence of Choices of the Intersection Space Homology; 2.4 The Homotopy Type of Intersection Spaces for Interleaf Links; 2.5 The Middle Dimension; 2.6 Cap products for Middle Perversities; 2.7 L-Theory; 2.8 Intersection Vector Bundles and K-Theory; 2.9 Beyond Isolated Singularities; 3 String Theory; 3.1 Introduction3.2 The Topology of 3-Cycles in 6-Manifolds; 3.3 The Conifold Transition; 3.4 Breakdown of the Low Energy Effective Field Theory Near a Singularity; 3.5 Massless D-Branes; 3.6 Cohomology and Massless States; 3.7 The Homology of Intersection Spaces and Massless D-Branes; 3.8 Mirror Symmetry; 3.9 An Example; References; Index