Formally integrable complex structures on higher dimensional knot spaces

0544043 - MÚ 2022 RIV US eng J - Journal Article
Fiorenza, D. - Le, Hong-Van
Formally integrable complex structures on higher dimensional knot spaces.
Journal of Symplectic Geometry. Roč. 19, č. 3 (2021), s. 507-529. ISSN 1527-5256. E-ISSN 1540-2347
R&D Projects: GA ČR(CZ) GA18-00496S
Institutional support: RVO:67985840
Keywords : Riemannian manifold * higher dimensional space * Kähler manifold
OECD category: Pure mathematics
Impact factor: 0.725, year: 2021
Method of publishing: Limited access
https://dx.doi.org/10.4310/JSG.2021.v19.n3.a1

Let S be a compact oriented finite dimensional manifold and M a finite dimensional Riemannian manifold, let Immf(S,M) the space of all free immersions φ:S→M and let B+i,f(S,M) the quotient space Immf(S,M)/Diff+(S), where Diff+(S) denotes the group of orientation preserving diffeomorphisms of S. In this paper we prove that if M admits a parallel r-fold vector cross product χ∈Ωr(M,TM) and dimS=r−1 then B+i,f(S,M) is a formally Kähler manifold. This generalizes Brylinski’s, LeBrun’s and Verbitsky’s results for the case that S is a codimension 2 submanifold in M, and S=S1 or M is a torsion-free G2-manifold respectively.
Permanent Link: http://hdl.handle.net/11104/0321107