Geodesic
Contact manifolds with symplectomorphic symplectizations
Courte, Sylvain1
1 Unité de mathématiques pures et appliquées, ENS de Lyon, 46 allée d’Italie 69364, Lyon Cedex 07, France
Geometry & topology, Tome 18 (2014) no. 1, pp. 1-15.

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

We provide examples of contact manifolds of any odd dimension greater than or equal to 5 which are not diffeomorphic but have exact symplectomorphic symplectizations.

DOI : 10.2140/gt.2014.18.1
Classification : 53D10
Keywords: symplectization, Mazur trick, Weinstein cobordism, Whitehead torsion

Courte, Sylvain 1

1 Unité de mathématiques pures et appliquées, ENS de Lyon, 46 allée d’Italie 69364, Lyon Cedex 07, France 
@article{GT_2014_18_1_a0,
     author = {Courte, Sylvain},
     title = {Contact manifolds with symplectomorphic symplectizations},
     journal = {Geometry & topology},
     pages = {1--15},
     publisher = {mathdoc},
     volume = {18},
     number = {1},
     year = {2014},
     doi = {10.2140/gt.2014.18.1},
     url = {http://geodesic.mathdoc.fr/articles/10.2140/gt.2014.18.1/}
}
TY  - JOUR
AU  - Courte, Sylvain
TI  - Contact manifolds with symplectomorphic symplectizations
JO  - Geometry & topology
PY  - 2014
SP  - 1
EP  - 15
VL  - 18
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.2140/gt.2014.18.1/
DO  - 10.2140/gt.2014.18.1
ID  - GT_2014_18_1_a0
ER  - 
%0 Journal Article
%A Courte, Sylvain
%T Contact manifolds with symplectomorphic symplectizations
%J Geometry & topology
%D 2014
%P 1-15
%V 18
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.2140/gt.2014.18.1/
%R 10.2140/gt.2014.18.1
%F GT_2014_18_1_a0
Courte, Sylvain. Contact manifolds with symplectomorphic symplectizations. Geometry & topology, Tome 18 (2014) no. 1, pp. 1-15. doi : 10.2140/gt.2014.18.1. http://geodesic.mathdoc.fr/articles/10.2140/gt.2014.18.1/

[1] W Chen, Smooth $s$–cobordisms of elliptic $3$–manifolds, J. Differential Geom. 73 (2006) 413

[2] K Cieliebak, Y Eliashberg, From Stein to Weinstein and back: Symplectic geometry of affine complex manifolds, Amer. Math. Soc. Colloq. Pub. 59, Amer. Math. Soc. (2012)

[3] M M Cohen, A course in simple-homotopy theory, Graduate Texts in Mathematics 10, Springer (1973)

[4] Y Eliashberg, Symplectic geometry of plurisubharmonic functions, from: "Gauge theory and symplectic geometry" (editors J Hurtubise, F Lalonde, G Sabidussi), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci. 488, Kluwer Acad. Publ. (1997) 49

[5] Y Eliashberg, A Givental, H Hofer, Introduction to symplectic field theory, from: "Visions in Mathematics: GAFA 2000, Part II", Geom. Funct. Anal. special volume, Birkhäuser (2000) 560

[6] A Hatcher, T Lawson, Stability theorems for “concordance implies isotopy” and “$h$–cobordism implies diffeomorphism”, Duke Math. J. 43 (1976) 555

[7] M A Kervaire, Le théorème de Barden–Mazur–Stallings, Comment. Math. Helv. 40 (1965) 31

[8] J Milnor, Two complexes which are homeomorphic but combinatorially distinct, Ann. of Math. 74 (1961) 575

[9] J Milnor, Lectures on the $h$–cobordism theorem, Princeton Univ. Press (1965)

[10] J Milnor, Whitehead torsion, Bull. Amer. Math. Soc. 72 (1966) 358

[11] E Murphy, Loose legendrian embeddings in high dimensional contact manifolds

[12] A Ranicki, Algebraic and geometric surgery, Oxford University Press (2002)

[13] S Smale, On the structure of manifolds, Amer. J. Math. 84 (1962) 387

Cité par Sources :