Let M('n+k) be an open PL manifold of dimension n + k (GREATERTHEQ) 6, let X be a finite polyhedron, and suppose f:M('n+k )(--->)(' )X(' )x R('k) is a bounded homotopy equivalence. If k (GREATERTHEQ) 1, we use radial engulfing and Siebenmann's twist-gluing (twist = id.) to construct a manifold M(,1) with infinite cyclic cover M and a bounded homotopy equivalence f(,1):M(,1) (--->) X x S('1) x R('k-1). By iterating this construction we obtain a manifold M(,k-1) and a bounded homotopy equivalence f(,k-1):M(,k-1) (--->) X x S('1) x ... x S('1) x R. We show that the Siebenmann obstruction in (')K(,0)(Z(pi)(,1)M(,k-1)) to factoring M(,k-1) = N(,k-1) x R is an element of (')K(,-k+1)(Z(pi)(,1)X). Thus we get a sequence of obstructions (sigma)(,i) (ELEM) K(,-i+1)(Z(pi)(,1)X) , j (LESSTHEQ) i (LESSTHEQ) k, such that M = Y x R('k-j+1), for some PL manifold Y, if and only if each (sigma)(,i) is 0. / Source: Dissertation Abstracts International, Volume: 44-06, Section: B, page: 1858. / Thesis (Ph.D.)--The Florida State University, 1983.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_75117 |
| Contributors | PACHECO, PETER S., Florida State University |
| Source Sets | Florida State University |
| Detected Language | English |
| Type | Text |
| Format | 82 p. |
| Rights | On campus use only. |
| Relation | Dissertation Abstracts International |
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