Geodesic
Equivariant corks
Auckly, Dave1 ; Kim, Hee Jung2 ; Melvin, Paul3 ; Ruberman, Daniel4
1Department of Mathematics, Kansas State University, Manhattan, KS 66506, United States
2Department of Mathematical Sciences, Seoul National University, Seoul 151-747, South Korea
3Department of Mathematics, Bryn Mawr College, Bryn Mawr, PA 19010, United States
4Department of Mathematics, Brandeis University, MS 050, Waltham, MA 02454, United States
Algebraic and Geometric Topology, Tome 17 (2017) no. 3, pp. 1771-1783
Cet article a éte moissonné depuis la source Mathematical Sciences Publishers

Voir la notice de l'article

For any finite subgroup G of SO(4), we construct a contractible 4–manifold C, with an effective G–action on its boundary, that can be embedded in a closed 4–manifold so that cutting C out and regluing using distinct elements of G will always yield distinct smooth 4–manifolds.

DOI : 10.2140/agt.2017.17.1771
Classification : 57M99, 57R55
Keywords: corks, smooth structures on 4-manifolds

Auckly, Dave  1   ; Kim, Hee Jung  2   ; Melvin, Paul  3   ; Ruberman, Daniel  4

1 Department of Mathematics, Kansas State University, Manhattan, KS 66506, United States
2 Department of Mathematical Sciences, Seoul National University, Seoul 151-747, South Korea
3 Department of Mathematics, Bryn Mawr College, Bryn Mawr, PA 19010, United States
4 Department of Mathematics, Brandeis University, MS 050, Waltham, MA 02454, United States 
@article{10_2140_agt_2017_17_1771,
     author = {Auckly, Dave and Kim, Hee Jung and Melvin, Paul and Ruberman, Daniel},
     title = {Equivariant corks},
     journal = {Algebraic and Geometric Topology},
     pages = {1771--1783},
     year = {2017},
     volume = {17},
     number = {3},
     doi = {10.2140/agt.2017.17.1771},
     url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2017.17.1771/}
}
TY  - JOUR
AU  - Auckly, Dave
AU  - Kim, Hee Jung
AU  - Melvin, Paul
AU  - Ruberman, Daniel
TI  - Equivariant corks
JO  - Algebraic and Geometric Topology
PY  - 2017
SP  - 1771
EP  - 1783
VL  - 17
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.2140/agt.2017.17.1771/
DO  - 10.2140/agt.2017.17.1771
ID  - 10_2140_agt_2017_17_1771
ER  - 
%0 Journal Article
%A Auckly, Dave
%A Kim, Hee Jung
%A Melvin, Paul
%A Ruberman, Daniel
%T Equivariant corks
%J Algebraic and Geometric Topology
%D 2017
%P 1771-1783
%V 17
%N 3
%U http://geodesic.mathdoc.fr/articles/10.2140/agt.2017.17.1771/
%R 10.2140/agt.2017.17.1771
%F 10_2140_agt_2017_17_1771
Auckly, Dave; Kim, Hee Jung; Melvin, Paul; Ruberman, Daniel. Equivariant corks. Algebraic and Geometric Topology, Tome 17 (2017) no. 3, pp. 1771-1783. doi: 10.2140/agt.2017.17.1771

[1] S Akbulut, A fake compact contractible 4–manifold, J. Differential Geom. 33 (1991) 335

[2] S Akbulut, D Ruberman, Absolutely exotic compact 4–manifolds, Comment. Math. Helv. 91 (2016) 1 | DOI

[3] S Akbulut, K Yasui, Corks, plugs and exotic structures, J. Gökova Geom. Topol. 2 (2008) 40

[4] S Akbulut, K Yasui, Knotting corks, J. Topol. 2 (2009) 823 | DOI

[5] S Akbulut, K Yasui, Stein 4–manifolds and corks, J. Gökova Geom. Topol. 6 (2012) 58

[6] D Auckly, H J Kim, P Melvin, D Ruberman, From tangles to equivariant hyperbolic corks, AMS abstract (2016)

[7] Ž Bižaca, R E Gompf, Elliptic surfaces and some simple exotic R4’s, J. Differential Geom. 43 (1996) 458

[8] M Culler, N M Dunfield, J R Weeks, SnapPy, a computer program for studying the topology of 3–manifolds

[9] C L Curtis, M H Freedman, W C Hsiang, R Stong, A decomposition theorem for h–cobordant smooth simply-connected compact 4–manifolds, Invent. Math. 123 (1996) 343 | DOI

[10] R Fintushel, R J Stern, Rational blowdowns of smooth 4–manifolds, J. Differential Geom. 46 (1997) 181

[11] M H Freedman, The topology of four-dimensional manifolds, J. Differential Geom. 17 (1982) 357

[12] R E Gompf, Nuclei of elliptic surfaces, Topology 30 (1991) 479 | DOI

[13] R E Gompf, Infinite order corks, preprint (2016)

[14] R E Gompf, Infinite order corks via handle diagrams, preprint (2016)

[15] R E Gompf, A I Stipsicz, 4–manifolds and Kirby calculus, 20, Amer. Math. Soc. (1999) | DOI

[16] H Hendriks, Applications de la théorie d’obstruction en dimension 3, Bull. Soc. Math. France Mém. 53 (1977) 81

[17] R Matveyev, A decomposition of smooth simply-connected h–cobordant 4–manifolds, J. Differential Geom. 44 (1996) 571

[18] B Mazur, A note on some contractible 4–manifolds, Ann. of Math. 73 (1961) 221 | DOI

[19] M Tange, Finite order corks, preprint (2016)

[20] B Zimmermann, On the classification of finite groups acting on homology 3–spheres, Pacific J. Math. 217 (2004) 387 | DOI

Cité par Sources :