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Controlled homotopy equivalences and str...
Hegenbarth, Friedric...

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Controlled homotopy equivalences and structure sets of manifolds by Hegenbarth, Friedrich ( Author )
Lemonjar Open Access
N.A
10-09-2014
For a closed topological n--manifold K and a map p:K→B inducing an isomorphism π1(K)→π1(B), there is a canonicaly defined morphism b:Hn+1(B,K,L)→S(K), where L is the periodic simply-connected surgery spectrum and S(K) is the topological structure set. We construct a refinement a:H+n+1(B,K,L)→Sε,δ(K) in the case when p is UV1, and we show that a is bijective if B is a finite-dimensional compact metric ANR. Here, H+n+1(B,K,L)⊂Hn+1(B,K,L), and Sε,δ(K) is the controlled structure set. We show that the Pedersen-Quinn-Ranicki controlled surgery sequence is equivalent to the exact L-homology sequence of the map p:K→B, i.e. that Hn+1(B,L)→H+n+1(B,K,L)→Hn(K,L+)→Hn(B,L), L+→L, is the connected covering spectrum of L. By taking for B various stages of the Postnikov tower of K, one obtains an interesting filtration of the controlled structure set.
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Article
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36.88 KB
English
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MYR 0.01
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https://arxiv.org/abs/1409.2970
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