منابع مشابه
Cobordism Theory Using Steenrod Operations
In this paper I give new proofs of the structure theorems for the unoriented cobordism ring [12] and the complex cobordism ring [8, 131. The proofs are elementary in the sense that no mention of the Steenrod algebra or Adams spectral sequence is made. In fact, the only result from homotopy theory which is used in an essential way is the Serre finiteness theorem in order to know that the complex...
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The notion of cobordism is simple; two manifolds M and N are said to be cobordant if their disjoint union is the boundary of some other manifold. Given the extreme difficulty of the classification of manifolds it would seem very unlikely that much progress could be made in classifying manifolds up to cobordism. However, René Thom, in his remarkable, if unreadable, 1954 paper Quelques propriétés...
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We develop rigorous foundations for parametrized homotopy theory. After preliminaries on point-set topology, base change functors, and proper actions of non-compact Lie groups, we develop the homotopy theory of equivariant ex-spaces (spaces over and under a given space) and of equivariant parametrized spectra. We emphasize several issues of independent interest and include a good deal of new ma...
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In nature, one observes that a K-theory of an object is defined in two steps. First a “structured” category is associated to the object. Second, a K-theory machine is applied to the latter category that produces an infinite loop space. We develop a general framework that deals with the first step of this process. The K-theory of an object is defined via a category of “locally trivial” objects w...
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The purpose of this paper is to give the algebraic topological background for elliptic cohomology theory and to pose some number theoretic problems suggested by these concepts. Algebraic topologists study functors from the category of spaces to various algebraic categories. In particular there are functors to the category of graded rings called multiplicative generalized cohomology theories. (A...
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ژورنال
عنوان ژورنال: Annales de l’institut Fourier
سال: 1973
ISSN: 0373-0956
DOI: 10.5802/aif.456