Algebraic & Geometric Topology Volume 19, issue 3 (2019)

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On uniqueness of end sums and $1$–handles at infinity

Jack S Calcut and Robert E Gompf

Algebraic & Geometric Topology 19 (2019) 1299–1339

DOI: 10.2140/agt.2019.19.1299

Bibliography

1	D R Anderson, Homotopy type and obstructions to smoothing, Topology 7 (1968) 333 MR0233361
2	I Belegradek, Obstructions to nonpositive curvature for open manifolds, Proc. Lond. Math. Soc. 109 (2014) 763 MR3260293
3	J Bennett, Exotic smoothings via large ℝ⁴’s in Stein surfaces, PhD thesis, The University of Texas at Austin (2015)
4	J Bennett, Exotic smoothings via large ℝ⁴’s in Stein surfaces, Algebr. Geom. Topol. 16 (2016) 1637 MR3523051
5	Ž Bižaca, R E Gompf, Elliptic surfaces and some simple exotic ℝ⁴’s, J. Differential Geom. 43 (1996) 458 MR1412675
6	M Brown, Locally flat imbeddings of topological manifolds, Ann. of Math. 75 (1962) 331 MR0133812
7	J S Calcut, P V Haggerty, Connected sum at infinity and 4–manifolds, Algebr. Geom. Topol. 14 (2014) 3281 MR3302962
8	J S Calcut, H C King, L C Siebenmann, Connected sum at infinity and Cantrell–Stallings hyperplane unknotting, Rocky Mountain J. Math. 42 (2012) 1803 MR3028764
9	J C Cantrell, Separation of the n–sphere by an (n−1)–sphere, Trans. Amer. Math. Soc. 108 (1963) 185 MR0155308
10	K Cieliebak, Y Eliashberg, From Stein to Weinstein and back : symplectic geometry of affine complex manifolds, 59, Amer. Math. Soc. (2012) MR3012475
11	R Connelly, A new proof of Brown’s collaring theorem, Proc. Amer. Math. Soc. 27 (1971) 180 MR0267588
12	J Dancis, General position maps for topological manifolds in the 2 3rds range, Trans. Amer. Math. Soc. 216 (1976) 249 MR0391098
13	D A Edwards, H M Hastings, Čech and Steenrod homotopy theories with applications to geometric topology, 542, Springer (1976) MR0428322
14	M H Freedman, F Quinn, Topology of 4–manifolds, 39, Princeton Univ. Press (1990) MR1201584
15	M H Freedman, L R Taylor, A universal smoothing of four-space, J. Differential Geom. 24 (1986) 69 MR857376
16	H Freudenthal, Über die Enden topologischer Räume und Gruppen, Math. Z. 33 (1931) 692 MR1545233
17	R Geoghegan, Topological methods in group theory, 243, Springer (2008) MR2365352
18	R E Gompf, Three exotic ℝ⁴’s and other anomalies, J. Differential Geom. 18 (1983) 317 MR710057
19	R E Gompf, An infinite set of exotic ℝ⁴’s, J. Differential Geom. 21 (1985) 283 MR816673
20	R E Gompf, A moduli space of exotic ℝ⁴’s, Proc. Edinburgh Math. Soc. 32 (1989) 285 MR1001127
21	R E Gompf, Constructing Stein manifolds after Eliashberg, from: "New perspectives and challenges in symplectic field theory" (editors M Abreu, F Lalonde, L Polterovich), CRM Proc. Lecture Notes 49, Amer. Math. Soc. (2009) 229 MR2555939
22	R E Gompf, Minimal genera of open 4–manifolds, (2013) arXiv:1309.0466v2
23	R E Gompf, Minimal genera of open 4–manifolds, Geom. Topol. 21 (2017) 107 MR3608710
24	R E Gompf, Quotient manifolds of flows, J. Knot Theory Ramifications 26 (2017) MR3604487
25	R E Gompf, Group actions, corks and exotic smoothings of ℝ⁴, Invent. Math. 214 (2018) 1131 MR3878728
26	R E Gompf, A I Stipsicz, 4–manifolds and Kirby calculus, 20, Amer. Math. Soc. (1999) MR1707327
27	M W Hirsch, Differential topology, 33, Springer (1994) MR1336822
28	T Homma, On the imbedding of polyhedra in manifolds, Yokohama Math. J. 10 (1962) 5 MR0154287
29	B Hughes, A Ranicki, Ends of complexes, 123, Cambridge Univ. Press (1996) MR1410261
30	M A Kervaire, J W Milnor, Groups of homotopy spheres, I, Ann. of Math. 77 (1963) 504 MR0148075
31	R C Kirby, L C Siebenmann, Foundational essays on topological manifolds, smoothings, and triangulations, Princeton Univ. Press (1977) MR0645390
32	K W Kwun, F Raymond, Mapping cylinder neighborhoods, Michigan Math. J. 10 (1963) 353 MR0156324
33	B Mazur, On embeddings of spheres, Bull. Amer. Math. Soc. 65 (1959) 59 MR0117693
34	M L Mihalik, Semistability at the end of a group extension, Trans. Amer. Math. Soc. 277 (1983) 307 MR690054
35	R Myers, End sums of irreducible open 3–manifolds, Quart. J. Math. Oxford Ser. 50 (1999) 49 MR1673256
36	F Quinn, Ends of maps, III : Dimensions 4 and 5, J. Differential Geom. 17 (1982) 503 MR679069
37	P Sparks, The double n–space property for contractible n–manifolds, Algebr. Geom. Topol. 18 (2018) 2131 MR3797063
38	J R Stallings, On infinite processes leading to differentiability in the complement of a point, from: "Differential and combinatorial topology" (editor S S Cairns), Princeton Univ. Press (1965) 245 MR0180983
39	L R Taylor, An invariant of smooth 4–manifolds, Geom. Topol. 1 (1997) 71 MR1483766
40	F C Tinsley, D G Wright, Some contractible open manifolds and coverings of manifolds in dimension three, Topology Appl. 77 (1997) 291 MR1451590