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687 pages, 21Mb PDF, free downloads, September 10, 2009

Abstract:

Fundamental concepts of: Algebraic Topology, Quantum Physics, Category Theory and Higher Dimensional Algebra. A detailed Contents Table follows:========================================== Contents: Contributed Articles: Algebra 1 Abstract Algebra 7 Algebraic logic 10 Galois group 13 Galois theory 14 Grothendieck's Galois theory 20 Algebraic Topology 21 Table of contents 21 Algebraic topology 21 Open set 26 Topology 29 Topological property 35 Topological space 38 Continuous function (topology) 43 Fibration 46 Homeomorphism 48 Compact space 51 Hausdorff space 58 Tangent space 61 Metric space 64 Riemannian manifold 73 Kahler manifold 78 Calabi--Yau manifold 80 Pseudo-- Riemannian manifold 84 Hypersurface 86 CR manifold 86 Symplectic manifold 90 Betti number 93 Euler characteristic 95 Presheaf (category theory) 102 Sheaf (mathematics) 102 Postnikov system 112 Grothendieck topology 113 Groupoid 119 Lie groupoid 124 Lie algebroid 125 Algebroid 127 Space group 128 Fundamental group 135 Homotopy 140 Crossed module 144 Homology (mathematics) 146 Cohomology 149 Homology theory 152 Chain complex 154 Crystalline cohomology 156 Homological algebra 160 Algebraic K-- theory 163 Topological K-- theory 168 Stack (descent theory) 170 Esquisse d'un Programme 171 Important Theorems in Algebraic Topology 176 Hairy ball theorem 176 Universal coefficient theorem 178 Borsuk-- Ulam theorem 179 Brouwer fixed point theorem 180 Cellular approximation theorem 191 Eilenberg--Zilber theorem 192 Hurewicz theorem 193 Kenneth theorem 195 Poincare' duality theorem 197 Tychonoff's theorem 200 Tietze extension theorem 202 Universal coefficient theorem 203 Seifert---Brown--van Kampen theorem 204 Whitehead theorem 208 List of important publications in mathematics 209 Higher Dimensional Algebra 233 Higher-- dimensional algebra 233 Higher category theory 236 Enriched category 237 Graph theory 239 Graph coloring 248 Multicategory 261 Metatheory 262 Metalogic 264 Metamathematics 267 Category theories 269 Category theory 269 Algebraic category 276 Categorical logic 278 Category (mathematics) 281 Abelian category 285 Topos 288 Heyting algebra 293 Subobject classifier 302 Generator 305 Exact sequence 306 Coproduct 309 Product 312 Pushout 313 Pullback 313 Limit 314 Colimit 315 Yoneda lemma 324 Functor 326 Adjoint functors 330 Representable functor 344 Functor category 346 Natural equivalence 348 Natural transformation 351 Dual (category theory) 354 Isomorphism 356 Semigroup 359 Monoid 364 Domain theory 369 Baire category theorem 374 Algebraic Quantum Topology 376 Lagrangian mechanics 376 Hamiltonian mechanics 387 Noether's theorem 395 Quantum theory 409 Observable 409 Wave function 411 Rigged Hilbert space 416 Kac--Moody algebra 418 Operator algebra 420 Clifford algebra 421 Von Neumann algebra 431 C*- algebra 442 Jones polynomial 447 Subfactor 449 Quantum logic 451 Quantum group 458 Hopf algebra 466 Quasitriangular Hopf algebra 469 Quantum double 470 Grassman algebra 472 Special unitary group 485 Gauge theory 491 Yang--Mills theory 502 Yangian 506 Superalgebra 508 Supergroup 511 Symmetry breaking 511 Spontaneous symmetry breaking 512 Goldstone boson 515 Higgs boson 519 Higgs mechanism 525 Topological order 533 Topological quantum field theory 539 Noncommutative geometry 542 Noncommutative quantum field theory 546 Noncommutative standard model 548 Quantum geometry 549 Fuzzy sphere 550 Quantum torus 551 Geometrodynamics 553 Quantum gravity 555 Homological mirror symmetry 565 Notable Algebraic Topologists and Category Theoreticians 567 Michael Atiyah 567 Karol Borsuk 586 Nicolas Bourbaki 587 Ronald Brown (mathematician) 592 Henri Cartan 599 Alain Connes 602 Jean Dieudonne' 604 Charles Ehresmann 607 Samuel Eilenberg 609 Peter J. Freyd 611 Alexander Grothendieck 612 Heinz Hopf 620 Egbert van Kampen 622 Maxim Kontsevich 623 Otto Hermann Kenneth 624 Saunders Mac Lane 625 William Lawvere 627 Barry Mitchell 629 Roger Penrose 630 Grigori Perelman 637 Nicolae Popescu 643 Nicolas Rashevsky 649 Robert Rosen 654 Jean- Pierre Serre 658 J. H. C. Whitehead 662 Edward Witten 665 References Article Sources and Contributors 668 Image Sources, Licenses and Contributors 677 Article Licenses License 680 http://en.wikipedia.org/wiki/User:Bci2/Books/AlgebraicTopologyv1#Algebraic_Topology.2C_Category_Theory_and_Higher_Dimensional_Algebra-Results_and_Applications_to_Quantum_Physics

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open access: GNU License / Creative Commons Attribution-Share Alike 3.0 http://en.wikipedia.org/wiki/User:Bci2/Books/AlgebraicTopologyv1#Algebraic_Topology.2C_Category_Theory_and_Higher_Dimensional_Algebra-Results_and_Applications_to_Quantum_Physics http://en.wikipedia.org/w/index.php?title=Special:Book/download/&collection_id=6e829d124c5461d2&writer=rl&return_to=User%3ABci2%2FBooks%2FAlgebraicTopologyv1 Copyright@2009 Bci2 and bci1, Edited and originated by Bci2- with several contributors listed before the License Statement by bci1 and Bci2: Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version ;published by the Free Software Foundation, with no Invariant Sections, no Front-Cover Texts, and no Back- Cover Texts. A copy of the license is included in the section entitled "GNU Free Documentation License". Edited by Bci2, with all contributors listed before the License statement.

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