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
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.
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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