By Edited by R. H. Fox, D. C. Spencer, A. W. Tucker

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**Extra info for Algebraic Geometry and Topology: A Symposium in Honor of S. Lefschetz**

**Sample text**

Suppose K is an n-dimensional sphere and L is a closed subcomplex. 1) K In this case L is not a regular boundary, and * is not a deformation K. However, it is a deformation retract of the open set L. This is easily seen if one observes that each simplex of K' which is neither in L' nor in K* is the join of a simplex cr of L' with a simplex r contained in K*. 2) H*-*(K - L) r. Therefore the LEFSCHETZ AND ALGEBRAIC TOPOLOGY Since K L an open is set, 33 the type of cohomology group must be specified.

Sci. , 15: 367-369. [43] Ge"orne*trie sur les Surfaces et les Varie*t6s Alge"briques. Villars. 1930 [45] Topology. New York, American Mathematical Society, ix, 410pp. (Colloquium Publications, vol. ) [46] Les transformations continues des ensembles fermes et leurs points fixes. Acad. des Sci. Paris. , 190: 99-100. [47] On the duality theorems for the Betti numbers of topological manifolds (with W. W. Flexner). Proc. Nat. Acad. Sci. , 16: 530-533. [48] On transformations of closed sets. Ann. of Math.

This is easily seen if one observes that each simplex of K' which is neither in L' nor in K* is the join of a simplex cr of L' with a simplex r contained in K*. 2) H*-*(K - L) r. Therefore the LEFSCHETZ AND ALGEBRAIC TOPOLOGY Since K L an open is set, 33 the type of cohomology group must be specified. 2) gives cohomology group. the Lefschetz duality Hq (K/L) & H*-+(K - L) (8-3) based only on the weaker assumption that The K - L is an open manifold. 4) The Hq (K) -> H (K/L) -> H^(L) -> Hq^(K) -.

### Algebraic Geometry and Topology: A Symposium in Honor of S. Lefschetz by Edited by R. H. Fox, D. C. Spencer, A. W. Tucker

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