Classifies diffeomorphism types and Euler characteristics of manifolds with boundary admitting submersions with definite folds (including round and image-simple variants) into R^n, with applications to non-singular extensions.
Hempel,Some3-manifold groups with the same finite quotients, arXiv:1409.3509v2, preprint
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abstract
We give examples of closed, oriented 3-manifolds whose fundamental groups are not isomorphic, but yet have the same sets of finite quotient groups; hence the same profinite completions. We also give examples of compact, oriented 3-manifolds with non-empty boundaries whose fundamental groups though isomorphic have distinct peripheral structures, but yet have the same sets of finite peripheral pair quotients (defined below). The examples are Seifert Fibered Spaces with zero rational Euler number; moreover most of these manifolds give rise to such examples.
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On submersions with definite folds of manifolds with boundary into Euclidean spaces
Classifies diffeomorphism types and Euler characteristics of manifolds with boundary admitting submersions with definite folds (including round and image-simple variants) into R^n, with applications to non-singular extensions.