Technical Books

This PDF book covers the following topics related to Geometry, Introduction, Construction of the Euclidean plane, Transformations, Tricks of the trade, Concurrence and collinearity, Circular reasoning, Triangle trivia, Quadrilaterals, Geometric inequalities, Inversive and hyperbolic geometry, Projective geometry.

This PDF book covers the following topics related to Geometry, The Five Groups of Axioms, the Compatibility and Mutual Independence of the Axioms, the Theory of Proportion, the Theory of Plane Areas, Desarguess Theorem, Pascals Theorem, Geometrical Constructions Based Upon the Axioms IV.

This note contains below topics, it is lc or dlt i each coecient of B is, It is klt i each of coecient of B is, It is canonical or terminal i B, The latter paper also settles most cases in dimension.

This note contains below topics, Morita equivalence, Derivations and Atiyah algebras, The Bar complex, Hochschild homology and cohomology, Poisson brackets and Gerstenhaber algebras, Deformation quantization, K ahler differentials, The HochschildKostantRosenberg Theorem, Noncommutative differential forms, Noncommutative Calculus, The Representation functor.

These notes study symplectic structures on graded manifolds and their global counterparts, higher Lie groupoids. They start with graded manifolds, then symplectic Q manifolds and Lagrangian Q submanifolds, and then the shifted symplectic structure on higher Lie groupoids.

This note contains below topics, Calculus of variations, Review of differential calculus on Banach spaces, The minimum problem, EulerLagrange equations in finite dimension, Hamiltonian description, The Noether theorem, The Linear Sigma model, Hadamard s variation formula for the Green s function, Symplectic Geometry, Symplectic Manifolds, Symplectic form on the Cotangent Bundle of a Manifold, Finslerian Geometry, Finsler Metric, Formulas in Riemannian Geometry, Review of Tensor calculus, Locally Minkowski space.

This note contains below topics, The Courant bracket Bfields and metrics, Spinors twists and skew torsion, Generalized complex manifolds, Generalized Kahler manifolds, Generalized holomorphic bundles, Holomorphic bundles and the Bfield action.

This note contains below topics, and promote it to spin structures and spinor b undles over manifolds In, The precise analytical denitions will be given in, Indices indicating t he grading are always understood mod, The complex volume element is independent of the choice of basis.

This note contains below topics, Solutions of Jacobi Equations, Model Spaces Hessian Cosine Law, Local Comparison Theorems, Global Toponogov Comparison Theorems, Appliction of Toponogov s Comparison Theorem, Manifolds of Nonnegative Curvature, CheegerGromoll Soul Theorem, CheegerGromoll Soul Conjecture, CheegerGromoll Splitting Theorem, CheegerGromoll Covering Theorem, BishopGromov Volume Comparison, GromovHausdorff Convergence of Metric Spaces, Alexandrov Spaces, GrovePeterson Homotopy Type Theorem.

The aim of this book is to introduce hyperbolic geometry and its applications to twoand threemanifolds topology. Topics covered includes, Hyperbolic geometry, Hyperbolic space, Hyperbolic manifolds, Thickthin decomposition, The sphere at infinity, Surfaces, Teichmuller space, Topology of threemanifolds, Seifert manifolds, Constructions of threemanifolds, Threemanifolds, Mostow rigidity theorem, Hyperbolic Dehn filling.

This PDF book covers the following topics related to Geometric Topology, Algebraic Constructions, Homotopy Theoretical Localization, Completions in Homotopy Theory, Spherical Fibrations, Algebraic Geometry, The Galois Group in Geometric Topology.

This PDF book covers the following topics related to Geometric Topology, Klees Trick, Manifold factors, Stable homeomorphisms and the annulus conjecture, Cellular homology, Some elementary homotopy theory, Walls finiteness obstruction, A weak Poincare Conjecture in high dimensions, Stallings characterization of euclidean space, Whitehead torsion, Siebenmanns Thesis, Torus trickery 101 local contractibility, Torus trickery 102 the Annulus Conjecture, Homotopy structures on manifolds, etc.

This note covers the following topics, Walls finiteness obstruction, The whitehead torsion, The s cobordism theorem, Siebenmanns end theorem, Fibering over a circle.

This book contains below topics, Geometric preliminaries, Gromov Thurston examples, A convexity theorem, Products of matrices, Construction of convex projective structures on Gromov Thurston manifolds, Dual complex to the conical stratification of an affine manifold.

This note explans the following topics: Vector space Vn over scalars such as IR, The clifford geometric products, Inner and outer products, Bivectors in the standard model, Bivectors in the homogeneous model, Perpendicularity, Reflection through communication, Duality and subspace representation.