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Four-manifolds of large negative deficiency

Published online by Cambridge University Press:  03 February 2005

CHARLES LIVINGSTON
CHARLES LIVINGSTON
Affiliation:
Department of Mathematics, Indiana University, Bloomington, IN 47405, U.S.A. e-mail: livingst@indiana.edu
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Abstract

For every $N > 0$ there exists a group of deficiency less than ${-}N$ that arises as the fundamental group of a smooth homology 4-sphere and also as the fundamental group of the complement of a compact contractible submanifold of the 4-sphere. A group is the fundamental group of the complement of a contractible submanifold of the $n$-sphere, $n > 4$, if and only if it is the fundamental group of a homology $n$-sphere. There exist fundamental groups of homology $n$-spheres, $n > 4$, that cannot arise as the fundamental group of the complement of a contractible submanifold of the 4-sphere.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 138 , Issue 1 , January 2005 , pp. 107 - 115
Copyright
2005 Cambridge Philosophical Society

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