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

Geometric Topology · Submitted 1 Jun 2000

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim One proves that there exists an obstruction to an open simply connected $n$-manifold of dimension $n\geq 5$ being geometrically simply connected.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,206 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.76 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.43 · compares with prior results 0.27 · mentions code or data availability 0.01.

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arXiv listing abstract v3. Results and the main claim are underlined; show every role.

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 Po\'enaru's conjecture.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	One proves that there exists an obstruction to an open simply connected $n$-manifold of dimension $n\geq 5$ being geometrically simply connected.	result 0.95	0.89	0.78	asserted 1.00
s1	In particular there exist uncountably many simply connected $n$-manifolds which are not w.g.s.c.	result 0.87	0.82	0.28	asserted 1.00
s2	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.	result 0.98	0.88	0.22	asserted 1.00
s3	(for $n=4$ it is only end compressible).	limitation 0.80	0.43	0.04	asserted 0.98
s4	We analyze further the case $n=4$ and Po\'enaru's conjecture.	contribution 0.99	0.82	0.05	asserted 0.59

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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arXiv listing abstract v3

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The paper

Original 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 Po\'enaru's conjecture.

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