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Algebraic Topology

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

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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