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Homology of Cell Complexes by George E. Cooke, Ross L. Finney

By George E. Cooke, Ross L. Finney

Shipped from united kingdom, please let 10 to 21 company days for arrival. Homology of telephone Complexes. , paperback, in keeping with Lectures via Norman E. Steenrod. initial casual Notes of collage classes and Seminars in arithmetic. 256pp. ex. lib. reliable analyzing replica.

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Z , •.. z ) . o n For an alternative description of lens spaces, and for =re information, the reader should consult Hilton and 1'l ylie's Ho=logy The space denoted by Theory, page 223. cpl 8. S2n+ljsl Cpn. is called complex pro,jective n-space, and is The space is a 2-sphere. •. ,zk' O, •.. ,O)} of state a result which allows us to compute the ho=logy groups of and the inclusion certain spaces very quickly. of 81 . S2k+l n+l C . C s2n+l Ck + l Then 82. X 2k+l k+l S = C 2n+l nS is consistent with the action Thus we have a diagram of inclusions and projections: In Chapter VII, we define ho=logy groups f'or arbitrary spaces in such a way that whenever a space with the subspace carries a regular 83 .

E , An+l l 2 2 n < u+ 1 larges t integeT of a regular compl ex is a subcomplex. then 3. 6. COROLLARY. 7. OOROLIoARY. Ho (K) IKI RO(K) of Z I{here k no. of components of K. That is , if is homeomorphic to K ILl, ,t hen and L are complexes such Ho(K) ~ HO(L) . rhenever K DEFllUTIOH. A has a finite or Ide order them in a silIIple sequence union of L _ n l {Ln} inductively by Let j be the If j < n+ 1 , A. 1. contains contains T B. to The construction of a maximal t ree can be carried sequence of trees 4.

1 appears in Chapter IX. Let H2 "" 0 X. may in certain cases be computed from an irregular complex on is given by H But the ho=logy groups need not be computed from a regular complex on n C H3 "" Z . 2~1 denote complex n-space, and let sented as the unit sphere in HO "" Z , X agree with the Then for each q 2 Hq(X) q­ morphic to the free abelian group on the q-cells of' K ( p-l mi 1) 1 s# ~i=O ~ a = pso o of q-cell is contained in ° 2 sia - Ta ) = a2 defined for q cellular homology groups of t he complex.

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