A Geometric Approach to Homology TheoryCambridge University Press, 1976 - Всего страниц: 149 The purpose of these notes is to give a geometrical treatment of generalized homology and cohomology theories. The central idea is that of a 'mock bundle', which is the geometric cocycle of a general cobordism theory, and the main new result is that any homology theory is a generalized bordism theory. The book will interest mathematicians working in both piecewise linear and algebraic topology especially homology theory as it reaches the frontiers of current research in the topic. The book is also suitable for use as a graduate course in homology theory. |
Содержание
Introduction | 1 |
Homotopy functors | 4 |
Mock bundles | 19 |
Coefficients | 41 |
Geometric theories | 81 |
Equivariant theories and operations | 98 |
Sheaves | 113 |
The geometry of CW complexes | 131 |
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A Geometric Approach to Homology Theory S. Buoncristiano,Colin Patrick Rourke,Brian Joseph Sanderson Недоступно для просмотра - 1976 |
Часто встречающиеся слова и выражения
A-sets abelian groups Axiom ball bordant bordism bordism class bordism theory boundary C. P. Rourke canonical cap products cell complex Chapter cobordism with coefficients codimension cohomology cohomology theory collar cone construction Corollary CW complexes defined definition denote dimension element embedded equivalence equivariant example F Ker follows framed X manifolds framified set functor g₁ generalised geometric theory give homology theory homomorphism inclusion induced K₁ labelled Lemma linked resolution linked stack M₁ map f Math mock bundle morphism n)-manifold natural transformation normal bundle notation oriented pairs Poincaré duality polyhedra polyhedron projection Proof Proposition q)-mock bundle R-module regular neighbourhood relabelling Remark resolution of G restriction singularities spectral sequence stack strata stratum structure subcomplex subdivision submanifold Suppose given Thom class Thom isomorphism topology transversality theorem transverse map universal coefficient zero