Legendrian submanifolds with Hamiltonian isotopic symplectizations
Algebraic and Geometric Topology, Tome 16 (2016) no. 6, pp. 3641-3652
Cet article a éte moissonné depuis la source Mathematical Sciences Publishers

Voir la notice de l'article

In any closed contact manifold of dimension at least 11, we construct examples of closed Legendrian submanifolds which are not diffeomorphic but whose Lagrangian cylinders in the symplectization are Hamiltonian isotopic.

DOI : 10.2140/agt.2016.16.3641
Classification : 53D10
Keywords: symplectization, h-cobordism, Weinstein structure, h-principle

Courte, Sylvain  1

1 Department of Mathematics, Uppsala University, Box 480, 751 06 Uppsala, Sweden
@article{10_2140_agt_2016_16_3641,
     author = {Courte, Sylvain},
     title = {Legendrian submanifolds with {Hamiltonian} isotopic symplectizations},
     journal = {Algebraic and Geometric Topology},
     pages = {3641--3652},
     year = {2016},
     volume = {16},
     number = {6},
     doi = {10.2140/agt.2016.16.3641},
     url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2016.16.3641/}
}
TY  - JOUR
AU  - Courte, Sylvain
TI  - Legendrian submanifolds with Hamiltonian isotopic symplectizations
JO  - Algebraic and Geometric Topology
PY  - 2016
SP  - 3641
EP  - 3652
VL  - 16
IS  - 6
UR  - http://geodesic.mathdoc.fr/articles/10.2140/agt.2016.16.3641/
DO  - 10.2140/agt.2016.16.3641
ID  - 10_2140_agt_2016_16_3641
ER  - 
%0 Journal Article
%A Courte, Sylvain
%T Legendrian submanifolds with Hamiltonian isotopic symplectizations
%J Algebraic and Geometric Topology
%D 2016
%P 3641-3652
%V 16
%N 6
%U http://geodesic.mathdoc.fr/articles/10.2140/agt.2016.16.3641/
%R 10.2140/agt.2016.16.3641
%F 10_2140_agt_2016_16_3641
Courte, Sylvain. Legendrian submanifolds with Hamiltonian isotopic symplectizations. Algebraic and Geometric Topology, Tome 16 (2016) no. 6, pp. 3641-3652. doi: 10.2140/agt.2016.16.3641

[1] K Cieliebak, Y Eliashberg, From Stein to Weinstein and back, 59, Amer. Math. Soc. (2012) | DOI

[2] M M Cohen, A course in simple-homotopy theory, 10, Springer (1973) | DOI

[3] S Courte, Contact manifolds with symplectomorphic symplectizations, Geom. Topol. 18 (2014) 1 | DOI

[4] S Courte, Contact manifolds and Weinstein h-cobordisms, J. Symplectic Geom. 14 (2016) 657 | DOI

[5] T Ekholm, Rational symplectic field theory over Z2 for exact Lagrangian cobordisms, J. Eur. Math. Soc. 10 (2008) 641 | DOI

[6] T Ekholm, K Honda, T Kálmán, Legendrian knots and exact Lagrangian cobordisms, J. Eur. Math. Soc. 18 (2016) 2627 | DOI

[7] Y Eliashberg, S Ganatra, O Lazarev, Flexible Lagrangians, preprint (2015)

[8] Y Eliashberg, A Givental, H Hofer, Introduction to symplectic field theory, Geom. Funct. Anal. (2000) 560 | DOI

[9] Y Eliashberg, N Mishachev, Introduction to the h–principle, 48, Amer. Math. Soc. (2002) | DOI

[10] F T Farrell, W C Hsiang, H–cobordant manifolds are not necessarily homeomorphic, Bull. Amer. Math. Soc. 73 (1967) 741 | DOI

[11] A Haefliger, Plongements différentiables de variétés dans variétés, Comment. Math. Helv. 36 (1961) 47

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

[13] F Laudenbach, A proof of Reidemeister–Singer’s theorem by Cerf’s methods, Ann. Fac. Sci. Toulouse Math. 23 (2014) 197 | DOI

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

[15] E Murphy, Loose Legendrian embeddings in high-dimensional contact manifolds, preprint (2012)

[16] 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)" (editor S S Cairns), Princeton Univ. Press (1965) 245

Cité par Sources :