A controlled plus construction for crumpled laminations

Authors:
R. J. Daverman and F. C. Tinsley

Journal:
Trans. Amer. Math. Soc. **342** (1994), 807-826

MSC:
Primary 57N70; Secondary 54B15, 57M20, 57N35

DOI:
https://doi.org/10.1090/S0002-9947-1994-1182981-6

MathSciNet review:
1182981

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Abstract | References | Similar Articles | Additional Information

Abstract: Given a closed *n*-manifold *M* and a finitely generated perfect subgroup *P* of , we previously developed a controlled version of Quillen's plus construction, namely a cobordism (*W, M, N*) with the inclusion a homotopy equivalence and kernel of equalling the smallest normal subgroup of containing *P* together with a closed map such that is a closed *n*-manifold for every and, in particular, and . We accomplished this by constructing an acyclic map of manifolds having the right fundamental groups, and *W* arose as the mapping cylinder of *f* with a collar attached along *N*. The main result here presents a condition under which the desired controlled plus construction can still be accomplished in many cases even when contains no finitely generated perfect subgroups. By-products of these results include a new method for constructing wild embeddings of codimension one manifolds and a better understanding of perfect subgroups of finitely presented groups.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1994-1182981-6

Keywords:
Crumpled lamination,
degree one map,
almost acyclic,
perfect normal subgroup

Article copyright:
© Copyright 1994
American Mathematical Society