منابع مشابه
Duality, Manifolds and Some Algebraic Topology
This is a short note intended to explore the applications of duality theory to the study of manifolds. I discuss Alexander duality, Lefschetz duality and Poincare duality, along with applications to the study of compact connected orientable manifolds. 1. Manifolds and points 1.1. The core question. One of the questions we shall be interested in is: Given two manifolds M and N , what are the way...
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Here we study the deformations of associative submanifolds inside a G2 manifold M 7 with a calibration 3-form φ. A choice of 2-plane field Λ on M (which always exists) splits the tangent bundle of M as a direct sum of a 3-dimensional associate bundle and a complex 4-plane bundle TM = E ⊕ V, and this helps us to relate the deformations to SeibergWitten type equations. Here all the surveyed resul...
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Smooth manifolds of G2 holonomy, used to compactify M -theory to four dimensions, give only abelian gauge groups without charged matter multiplets. But singular G2-manifolds can give abelian or nonabelian gauge groups with chiral fermions. We describe the mechanism of anomaly cancellation in these models, using anomaly inflow from the bulk. We also compare the anomaly predictions to what has be...
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This manuscript will be published as Chapter 5 in Wiley’s textbook Mathematical Tools for Physicists, 2nd edition, edited by Michael Grinfeld from the University of Strathclyde. The chapter provides an introduction to the basic concepts of Algebraic Topology with an emphasis on motivation from applications in the physical sciences. It finishes with a brief review of computational work in algebr...
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ژورنال
عنوان ژورنال: Expositiones Mathematicae
سال: 2016
ISSN: 0723-0869
DOI: 10.1016/j.exmath.2015.03.004