Geodesic
On uniqueness of end sums and 1–handles at infinity
Calcut, Jack1 ; Gompf, Robert2
1 Department of Mathematics, Oberlin College, Oberlin, OH, United States
2 Department of Mathematics, The University of Texas at Austin, Austin, TX, United States
Algebraic and Geometric Topology, Tome 19 (2019) no. 3, pp. 1299-1339

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

For oriented manifolds of dimension at least 4 that are simply connected at infinity, it is known that end summing is a uniquely defined operation. Calcut and Haggerty showed that more complicated fundamental group behavior at infinity can lead to nonuniqueness. We examine how and when uniqueness fails. Examples are given, in the categories top, pl and diff, of nonuniqueness that cannot be detected in a weaker category (including the homotopy category). In contrast, uniqueness is proved for Mittag-Leffler ends, and generalized to allow slides and cancellation of (possibly infinite) collections of 0– and 1–handles at infinity. Various applications are presented, including an analysis of how the monoid of smooth manifolds homeomorphic to ℝ4 acts on the smoothings of any noncompact 4–manifold.

DOI : 10.2140/agt.2019.19.1299
Classification : 57N99, 57Q99, 57R99
Keywords: end sum, connected sum at infinity, Mittag-Leffler, semistable end, exotic smoothing

Calcut, Jack 1 ; Gompf, Robert 2

1 Department of Mathematics, Oberlin College, Oberlin, OH, United States
2 Department of Mathematics, The University of Texas at Austin, Austin, TX, United States 
@article{10_2140_agt_2019_19_1299,
     author = {Calcut, Jack and Gompf, Robert},
     title = {On uniqueness of end sums and 1{\textendash}handles at infinity},
     journal = {Algebraic and Geometric Topology},
     pages = {1299--1339},
     publisher = {mathdoc},
     volume = {19},
     number = {3},
     year = {2019},
     doi = {10.2140/agt.2019.19.1299},
     url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2019.19.1299/}
}
TY  - JOUR
AU  - Calcut, Jack
AU  - Gompf, Robert
TI  - On uniqueness of end sums and 1–handles at infinity
JO  - Algebraic and Geometric Topology
PY  - 2019
SP  - 1299
EP  - 1339
VL  - 19
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.2140/agt.2019.19.1299/
DO  - 10.2140/agt.2019.19.1299
ID  - 10_2140_agt_2019_19_1299
ER  - 
%0 Journal Article
%A Calcut, Jack
%A Gompf, Robert
%T On uniqueness of end sums and 1–handles at infinity
%J Algebraic and Geometric Topology
%D 2019
%P 1299-1339
%V 19
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.2140/agt.2019.19.1299/
%R 10.2140/agt.2019.19.1299
%F 10_2140_agt_2019_19_1299
Calcut, Jack; Gompf, Robert. On uniqueness of end sums and 1–handles at infinity. Algebraic and Geometric Topology, Tome 19 (2019) no. 3, pp. 1299-1339. doi: 10.2140/agt.2019.19.1299

Cité par Sources :