## Geometry & Topology

### Manifolds with non-stable fundamental groups at infinity, III

#### Abstract

We continue our study of ends non-compact manifolds. The over-arching aim is to provide an appropriate generalization of Siebenmann’s famous collaring theorem that applies to manifolds having non-stable fundamental group systems at infinity. In this paper a primary goal is finally achieved; namely, a complete characterization of pseudo-collarability for manifolds of dimension at least 6.

#### Article information

Source
Geom. Topol., Volume 10, Number 1 (2006), 541-556.

Dates
Accepted: 24 March 2006
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.gt/1513799714

Digital Object Identifier
doi:10.2140/gt.2006.10.541

Mathematical Reviews number (MathSciNet)
MR2224464

Zentralblatt MATH identifier
1130.57032

#### Citation

Guilbault, Craig R; Tinsley, Frederick C. Manifolds with non-stable fundamental groups at infinity, III. Geom. Topol. 10 (2006), no. 1, 541--556. doi:10.2140/gt.2006.10.541. https://projecteuclid.org/euclid.gt/1513799714

#### References

• T A Chapman, L C Siebenmann, Finding a boundary for a Hilbert cube manifold, Acta Math. 137 (1976) 171–208
• M M Cohen, A course in simple-homotopy theory, Springer, New York (1973)
• E H Connell, A topological $h$-cobordism theorem for $n\geq 5$, Illinois J. Math. 11 (1967) 300–309
• M H Freedman, F Quinn, Topology of 4-manifolds, Princeton Mathematical Series 39, Princeton University Press, Princeton, NJ (1990)
• C R Guilbault, Compactifications of manifolds with boundary, in progress
• C R Guilbault, 1038016
• C R Guilbault, Manifolds with non-stable fundamental groups at infinity, Geom. Topol. 4 (2000) 537–579
• C R Guilbault, F C Tinsley, Manifolds with non-stable fundamental groups at infinity. II, Geom. Topol. 7 (2003) 255–286
• S Kwasik, R Schultz, Desuspension of group actions and the ribbon theorem, Topology 27 (1988) 443–457
• J Milnor, Whitehead torsion, Bull. Amer. Math. Soc. 72 (1966) 358–426
• D Quillen, Cohomology of groups, from: “Actes du Congrès International des Mathématiciens (Nice, 1970), Tome 2”, Gauthier-Villars, Paris (1971) 47–51
• C P Rourke, B J Sanderson, Introduction to piecewise-linear topology, Springer Study Edition, Springer, Berlin (1982)
• L Siebenmann, The obstruction to finding a boundary for an open manifold of dimension greater than five, PhD thesis, Princeton University (1965)
• J R Stallings, On infinite processes leading to differentiability in the complement of a point, from: “Differential and Combinatorial Topology (A Symposium in Honor of Marston Morse)”, Princeton Univ. Press, Princeton, N.J. (1965) 245–254
• T W Tucker, Non-compact $3$-manifolds and the missing-boundary problem, Topology 13 (1974) 267–273
• C T C Wall, Finiteness conditions for ${\rm CW}$-complexes, Ann. of Math. $(2)$ 81 (1965) 56–69