We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Pseudoholomorphic curves on the LCS-fication of contact manifolds.
- Authors
Oh, Yong-Geun; Savelyev, Yasha
- Abstract
For each contact diffeomorphism ϕ : (Q, ξ) → (Q, ξ) of (Q, ξ), we equip its mapping torus Mϕ with a locally conformal symplectic form of Banyaga's type, which we call the lcs mapping torus of the contact diffeomorphism ϕ. In the present paper, we consider the product Q × S1 = Mid (corresponding to ϕ = id) and develop basic analysis of the associated J-holomorphic curve equation, which has the form ∂ ˉ π w = 0 , w ∗ λ ∘ j = f ∗ d θ for the map u = (w, f) : Σ ˙ → Q × S 1 for a λ-compatible almost complex structure J and a punctured Riemann surface (Σ ˙ , j). In particular, w is a contact instanton in the sense of [31], [32].We develop a scheme of treating the non-vanishing charge by introducing the notion of charge class in H 1 (Σ ˙ , Z) and develop the geometric framework for the study of pseudoholomorphic curves, a correct choice of energy and the definition of moduli spaces towards the construction of a compactification of the moduli space on the lcs-fication of (Q, λ) (more generally on arbitrary locally conformal symplectic manifolds).
- Subjects
SYMPLECTIC manifolds; TORUS; PSEUDOCONVEX domains; RIEMANN surfaces
- Publication
Advances in Geometry, 2023, Vol 23, Issue 2, p153
- ISSN
1615-715X
- Publication type
Article
- DOI
10.1515/advgeom-2023-0004