exotic spheres
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2020 ◽  
Vol 101 (3) ◽  
pp. 1173-1218 ◽  
Author(s):  
M. Behrens ◽  
M. Hill ◽  
M. J. Hopkins ◽  
M. Mahowald

2016 ◽  
Vol 08 (03) ◽  
pp. 375-397 ◽  
Author(s):  
Tobias Ekholm ◽  
Thomas Kragh ◽  
Ivan Smith

Let [Formula: see text]. We prove that the cotangent bundles [Formula: see text] and [Formula: see text] of oriented homotopy [Formula: see text]-spheres [Formula: see text] and [Formula: see text] are symplectomorphic only if [Formula: see text], where [Formula: see text] denotes the group of oriented homotopy [Formula: see text]-spheres under connected sum, [Formula: see text] denotes the subgroup of those that bound a parallelizable [Formula: see text]-manifold, and where [Formula: see text] denotes [Formula: see text] with orientation reversed. We further show that if [Formula: see text] and [Formula: see text] admits a Lagrangian embedding in [Formula: see text], then [Formula: see text]. The proofs build on [1] and [18] in combination with a new cut-and-paste argument; that also yields some interesting explicit exact Lagrangian embeddings, for instance of the sphere [Formula: see text] into the plumbing [Formula: see text] of cotangent bundles of certain exotic spheres. As another application, we show that there are re-parametrizations of the zero-section in the cotangent bundle of a sphere that are not Hamiltonian isotopic (as maps rather than as submanifolds) to the original zero-section.


2016 ◽  
Author(s):  
Nurfarisha ◽  
Adhitya Ronnie Effendie ◽  
Muhammad Farchani Rosyid

2015 ◽  
Vol 8 (2) ◽  
pp. 586-602 ◽  
Author(s):  
Georgios Dimitroglou Rizell ◽  
Jonathan David Evans
Keyword(s):  

2015 ◽  
Vol 272 ◽  
pp. 611-629 ◽  
Author(s):  
Chao Qian ◽  
Zizhou Tang

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