cajole
发表于 2025-3-28 14:41:36
Homology with Arbitrary Coefficient Groups,many facts that the reader must know by now. Nevertheless, there . some point to a systematic organization of the ideas involved, and certain new ideas and techniques are introduced. The remainder of the chapter is concerned with homology groups with arbitrary coefficients. These new homology groups
Factual
发表于 2025-3-28 19:40:11
The Homology of Product Spaces,Some of the most important theorems in the preceding chapters bear out this expectation : If . is a subspace of ., the exact homology sequence of the pair . describes the relations between the homology groups of . and the homology groups of .. If the space . is the union of two subspaces . and ., th
配置
发表于 2025-3-29 00:01:54
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NATTY
发表于 2025-3-29 04:58:35
Duality Theorems for the Homology of Manifolds,ey, , Chapter I). One of the main goals of this chapter will be to prove one of the oldest results of algebraic topology, the famous Poincaré duality theorem for compact, orientable manifolds. It is easy to state the Poincaré duality theorem but the proof is lengthy.
狗舍
发表于 2025-3-29 10:06:05
Cup Products in Projective Spaces and Applications of Cup Products, real projective spaces will be used to prove the famous Borsuk—Ulam theorem. Then we will introduce the mapping cone of a continuous map, and use it to define the Hopf invariant of a map ..... The proof of existence of maps of Hopf invariant 1 will depend on our determination of cup products in the
阴郁
发表于 2025-3-29 15:05:49
Textbook 1980y. is a continuation of t he author‘s earlier book, .Algebraic Topology: An Introduction, .which presents such important supplementary material as the theory of the fundamental group and a thorough discussion of 2-dimensional manifolds. However, this earlier book is not a prerequisite for understanding .Singular Homology Theory.. .
遗弃
发表于 2025-3-29 17:57:09
Homology with Arbitrary Coefficient Groups,s and techniques are introduced. The remainder of the chapter is concerned with homology groups with arbitrary coefficients. These new homology groups are a generalization of those we have considered up to now. In the application of homology theory to certain problems they are often convenient and sometimes necessary.