Combinatorial Geometry with Application to Field Theory
by Linfan Mao
Publisher: InfoQuest 2009
Number of pages: 499
This monograph is motivated with surveying mathematics and physics by CC conjecture, i.e., a mathematical science can be reconstructed from or made by combinatorialization. Topics covered in this book include fundamental of mathematical combinatorics, differential Smarandache n-manifolds, combinatorial or differentiable manifolds and submanifolds, Lie multi-groups, combinatorial principal fiber bundles, gravitational field, quantum fields with their combinatorial generalization, also with discussions on fundamental questions in epistemology.
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by Sigmundur Gudmundsson - Lund University
These notes introduce the beautiful theory of Gaussian geometry i.e. the theory of curves and surfaces in three dimensional Euclidean space. The text is written for students with a good understanding of linear algebra and real analysis.
by Dominic Joyce - arXiv
An introduction to Calabi-Yau manifolds and special Lagrangian submanifolds from the differential geometric point of view, followed by recent results on singularities of special Lagrangian submanifolds, and their application to the SYZ Conjecture.
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We discuss the solution theory of geometric wave equations as they arise in Lorentzian geometry: for a normally hyperbolic differential operator the existence and uniqueness properties of Green functions and Green operators is discussed.
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