On the geometric simple connectivity of open manifolds

Louis Funar; Siddhartha Gadgil

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On the geometric simple connectivity of open manifolds

Louis Funar·Siddhartha Gadgil

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Abstract

One proves that there exists an obstruction to an open simply connected $n$-manifold of dimension $n\geq 5$ being geometrically simply connected. In particular there exist uncountably many simply connected $n$-manifolds which are not w.g.s.c. One proves that for $n\neq 4$ an $n$-manifold proper homotopy equivalent to a w.g.s.c. polyhedron is w.g.s.c. (for $n=4$ it is only end compressible). We analyze further the case $n=4$ and Poénaru's conjecture.

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Louis Funar, Siddhartha Gadgil. 2004-01-28. On the geometric simple connectivity of open manifolds. https://arxiv.org/abs/math/0006003

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