User:Bci2/Books/AlgebraicTopologyv1

Algebraic Topology, Category Theory and Higher Dimensional Algebra-Results and Applications to Quantum Physics

 * Algebra
 * Algebra
 * Abstract Algebra
 * Algebraic logic
 * Galois group
 * Galois theory
 * Grothendieck's Galois theory


 * Algebraic Topology
 * Table of contents
 * Algebraic topology
 * Open sets
 * Topology
 * Topological property
 * Topological space
 * Continuous function (topology)
 * Fibration
 * Homeomorphism
 * Compact space
 * Hausdorff space
 * Tangent space
 * Metric space-Riemann space
 * Riemannian manifold
 * Kähler manifold
 * Calabi–Yau manifold
 * Pseudo-Riemannian manifold
 * Hypersurface
 * CR manifold
 * Symplectic manifold
 * Betti number
 * Euler characteristics
 * Presheaf (category theory)
 * Sheaf (mathematics)
 * Postnikov system
 * Grothendieck topology
 * Groupoid
 * Lie groupoid
 * Lie algebroid
 * Algebroid
 * Space group
 * Fundamental group
 * Homotopy
 * Crossed module
 * Homology (mathematics)
 * Cohomologygroup
 * Homology theory
 * Chain complex
 * Crystalline cohomology
 * Homological algebra
 * Algebraic K-theory
 * Topological K-theory
 * Stack (descent theory)
 * Esquisse d'un Programme


 * Important Theorems in Algebraic Topology
 * Hairy ball theorem
 * Universal coefficient theorem
 * Borsuk-Ulam theorem
 * Brouwer fixed point theorem
 * Cellular approximation theorem
 * Eilenberg–Zilber theorem
 * Hurewicz theorem
 * Künneth theorem
 * Poincaré duality theorem
 * Tychonoff's theorem
 * Tietze extension theorem
 * Universal coefficient theorem
 * Seifert–van Kampen theorem
 * Whitehead theorem
 * List of important publications in mathematics


 * Higher Dimensional Algebra
 * Higher-dimensional algebra
 * Higher category theory
 * Enriched category
 * Graph theory
 * Graph coloring-Colored graph
 * Multicategory
 * Metatheory
 * Metalogic
 * Metamathematics


 * Category theories
 * Category theory
 * Algebraic category
 * Categorical logic
 * Category (mathematics)
 * Abelian category
 * Topos
 * Heyting algebra
 * Subobject classifier
 * Generator
 * Exact sequence
 * Coproduct-Direct sum
 * Product
 * Pushout
 * Pullback
 * Limit
 * Colimit
 * Yoneda lemma
 * Functor
 * Adjoint functors
 * Representable functor
 * Functor category
 * Natural equivalence
 * Natural transformation
 * Dual (category theory)
 * Isomorphism
 * Semigroup
 * Monoid
 * Domain theory
 * Baire category theorem


 * Algebraic Quantum Topology
 * Lagrangian mechanics
 * Hamiltonian mechanics
 * Noether's theorem
 * Quantum theory
 * Observable
 * Wave function
 * Rigged Hilbert space
 * Kac–Moody algebra
 * Operator algebra
 * Clifford algebra
 * von Neumann algebra
 * C*-algebra
 * Jones polynomial
 * Subfactor(Jones)
 * Quantum logic
 * Quantum group
 * Hopf algebra
 * Quasitriangular Hopf algebra
 * Quantum doubleconstruction
 * Grassman algebra
 * Special unitary group(SUn)
 * Gauge theory
 * Yang–Mills theory
 * Yangian
 * Superalgebra
 * Supergroup
 * Symmetry breaking
 * Spontaneous symmetry breaking
 * Goldstone bosons
 * Higgs boson
 * Higgs mechanism
 * Topological order
 * Topological quantum field theory(TQFT)
 * Noncommutative geometry(NCG)
 * Noncommutative quantum field theory
 * Noncommutative standard model
 * Quantum geometry
 * Fuzzy spheres
 * Quantum torus-tori
 * Geometrodynamics
 * Quantum gravity
 * Homological mirror symmetry-Conjecture


 * Notable Algebraic Topologists and Category Theoreticians
 * Michael Atiyah-(Sir)
 * Karol Borsuk
 * Nicolas Bourbaki
 * Ronald Brown (mathematician)
 * Henri Cartan
 * Alain Connes
 * Jean Dieudonné
 * Charles Ehresmann
 * Samuel Eilenberg
 * Peter J. Freyd
 * Alexander Grothendieck
 * Heinz Hopf
 * Egbert van Kampen
 * Maxim Kontsevich
 * Otto Hermann Künneth
 * Saunders Mac Lane
 * William Lawvere
 * Barry Mitchell
 * Roger Penrose
 * Grigori Perelman
 * Nicolae Popescu
 * Nicolas Rashevsky
 * Robert Rosen
 * Jean-Pierre Serre
 * J. H. C. Whitehead
 * Edward Witten