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The classifying spaces for surgery and cobordism of manifolds
Authors: ---
ISBN: 0691082251 069108226X 1400881471 Year: 1979 Publisher: Princeton, N. J.

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Abstract

Beginning with a general discussion of bordism, Professors Madsen and Milgram present the homotopy theory of the surgery classifying spaces and the classifying spaces for the various required bundle theories. The next part covers more recent work on the maps between these spaces and the properties of the PL and Top characteristic classes, and includes integrality theorems for topological and PL manifolds. Later chapters treat the integral cohomology of BPL and Btop. The authors conclude with a discussion of the PL and topological cobordism rings and a construction of the torsion-free generators.

Keywords

Algebraic topology --- 515.16 --- Classifying spaces --- Cobordism theory --- Manifolds (Mathematics) --- Surgery (Topology) --- Differential topology --- Homotopy equivalences --- Topology --- Geometry, Differential --- Spaces, Classifying --- Fiber bundles (Mathematics) --- Fiber spaces (Mathematics) --- Topology of manifolds --- Classifying spaces. --- Cobordism theory. --- Manifolds (Mathematics). --- Surgery (Topology). --- 515.16 Topology of manifolds --- Bijection. --- Calculation. --- Characteristic class. --- Classification theorem. --- Classifying space. --- Closed manifold. --- Cobordism. --- Coefficient. --- Cohomology. --- Commutative diagram. --- Commutative property. --- Complex projective space. --- Connected sum. --- Corollary. --- Cup product. --- Diagram (category theory). --- Differentiable manifold. --- Disjoint union. --- Disk (mathematics). --- Effective method. --- Eilenberg–Moore spectral sequence. --- Elaboration. --- Equivalence class. --- Exact sequence. --- Exterior algebra. --- Fiber bundle. --- Fibration. --- Function composition. --- H-space. --- Homeomorphism. --- Homomorphism. --- Homotopy fiber. --- Homotopy group. --- Homotopy. --- Hopf algebra. --- Iterative method. --- Loop space. --- Manifold. --- Massey product. --- N-sphere. --- Normal bundle. --- Obstruction theory. --- Pairing. --- Permutation. --- Piecewise linear manifold. --- Piecewise linear. --- Polynomial. --- Prime number. --- Projective space. --- Sequence. --- Simply connected space. --- Special case. --- Spin structure. --- Steenrod algebra. --- Subset. --- Summation. --- Tensor product. --- Theorem. --- Topological group. --- Topological manifold. --- Topology. --- Total order. --- Variétés topologiques --- Topologie differentielle


Book
On group-theoretic decision problems and their classification
Author:
ISBN: 0691080917 1400881781 9780691080918 Year: 1971 Volume: 68 Publisher: Princeton (N.J.): Princeton university press,

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Abstract

Part exposition and part presentation of new results, this monograph deals with that area of mathematics which has both combinatorial group theory and mathematical logic in common. Its main topics are the word problem for groups, the conjugacy problem for groups, and the isomorphism problem for groups. The presentation depends on previous results of J. L. Britton, which, with other factual background, are treated in detail.

Keywords

Group theory --- 510.6 --- Mathematical logic --- 510.6 Mathematical logic --- Group theory. --- Logic, Symbolic and mathematical. --- Groupes, Théorie des --- Groups, Theory of --- Substitutions (Mathematics) --- Algebra --- Algebra of logic --- Logic, Universal --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Abelian group. --- Betti number. --- Characteristic function (probability theory). --- Characterization (mathematics). --- Combinatorial group theory. --- Conjecture. --- Conjugacy class. --- Conjugacy problem. --- Contradiction. --- Corollary. --- Cyclic permutation. --- Decision problem. --- Diffeomorphism. --- Direct product. --- Direct proof. --- Effective method. --- Elementary class. --- Embedding. --- Enumeration. --- Epimorphism. --- Equation. --- Equivalence relation. --- Exact sequence. --- Existential quantification. --- Finite group. --- Finite set. --- Finitely generated group. --- Finitely presented. --- Free group. --- Free product. --- Fundamental group. --- Fundamental theorem. --- Group (mathematics). --- Gödel numbering. --- Homomorphism. --- Homotopy. --- Inner automorphism. --- Markov property. --- Mathematical logic. --- Mathematical proof. --- Mathematics. --- Monograph. --- Natural number. --- Nilpotent group. --- Normal subgroup. --- Notation. --- Permutation. --- Polycyclic group. --- Presentation of a group. --- Quotient group. --- Recursive set. --- Requirement. --- Residually finite group. --- Semigroup. --- Simple set. --- Simplicial complex. --- Solvable group. --- Statistical hypothesis testing. --- Subgroup. --- Theorem. --- Theory. --- Topology. --- Transitive relation. --- Triviality (mathematics). --- Truth table. --- Turing degree. --- Turing machine. --- Without loss of generality. --- Word problem (mathematics). --- Groupes, Théorie des --- Décidabilité (logique mathématique)

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