Inductive Detection for Homotopy Equivalences of Manifolds |
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Authors: | Slawomir Kwasik and Reinhard Schultz |
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Institution: | (1) Department of Mathematics, Tulane University, New Orleans, LA, 70118, U.S.A.;(2) Department of Mathematics, Purdue University, West Lafayette, IN, 47907, U.S.A |
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Abstract: | Let f:M N be a homotopy equivalence of CAT manifolds M and N (CAT := PL, TOP or DIFF) with finite fundamental groups. Each subgroup H 1(M) determines a homotopy equivalence fH:MH NH of the corresponding covering spaces. Suppose now that for each subgroup H in some particular class C (for example: elementary, hyperelementary or solvable) fH is homotopic to a CAT isomorphism. The general problem studied in this paper can be formulated as follows: If each map fH as above is homotopic to a CAT isomorphism, under what additional conditions on M, C and CAT is f itself (or f × idR) homotopic (properly homotopic) to a CATisomorphism? |
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Keywords: | homotopy equivalence infinite loop space manifold smoothing surgery theory |
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