2016/05/25 by Alexander Fauck, Fauck, Alexander · 2 citations
Mathematics · #37J55 (Secondary) #53D40 (Primary) 57R17 #57R65 #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.1605.07892
openalex publication_date 2016/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This thesis considers fillable contact structures on odd-dimensional manifolds. For that purpose, Rabinowitz-Floer homology (RFH) is used which was introduced by Cieliebak and Frauenfelder in 2009. A major part of the thesis is devoted to technical problems in the definition of RFH. In particular, it is shown that the moduli spaces involved are cut out transversally. Moreover, it is proved that RFH is essentially invariant under subcritical handle attachment. Finally, RFH is calculated for some Brieskorn manifolds. The obtained results are then used to show for every manifold, which supports fillable contact structures, that there exist either infinitely many different fillable contact structures, or one contact structure with infinitely many different fillings or for every fillable contact structure holds that RFH is infinite dimensional in every degree.