$L_{\infty}$-Kuranishi spaces and the moduli space of pseudoholomorphic disks

Taesu Kim

Home/Archive/arXiv

arXiv · 2511.05206

$L_{\infty}$-Kuranishi spaces and the moduli space of pseudoholomorphic disks

Taesu Kim

View original source ↗Read source document ↗Export metadata ↓

Abstract

We show that the moduli space of pseudoholomorphic disks is an example of the $L_{\infty}$-Kuranishi spaces introduced in \cite{Kim1}, provided that a condition for the existence of a stratification with a system of tubular neighborhoods holds on each chart. With respect to this structure, the forgetful and evaluation maps for the moduli space lift to morphisms between $L_{\infty}$-Kuranishi spaces.

Explore related subjects

math.SG

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Taesu Kim. 2026-06-23. $L_{\infty}$-Kuranishi spaces and the moduli space of pseudoholomorphic disks. https://arxiv.org/abs/2511.05206

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Surjectivity of real-linear Cauchy--Riemann operators: from the minimal Harder--Narasimhan slope to automatic transversality

This paper relates the minimal Harder--Narasimhan slope to the surjectivity of real-linear Cauchy--Riemann operators. We establish a conformally invariant $L^2$ criterion and an asymptotic slope criterion, which yield higher-rank automatic transversality criteria for pseudoholomorphic curves beyond the classical rank-one framework. Applications to pseudoholomorphic spheres in $S^6$ provide quantitative $L^2$ obstructions to the integrability of almost complex structures.

math.SG↗

arXiv2026

Welschinger invariants and the Conway polynomial

Welschinger showed that counts of connected holomorphic disks with Lagrangian boundary in symplectic 6-manifolds, meeting at least one boundary constraint, can be made invariant by correcting them with counts of disconnected disks weighted by certain "self-linking" numbers. We show his invariant is the lowest order term in an all-genus curve count where curves are weighted by the Conway polynomials of their boundaries. This in turn is a specialization of the skein-valued curve count, but can be defined without the 4-chain and vector field used in that setup.

math.SG↗

arXiv2026

KAM splittings and equidistributed periodic orbits for stable hypersurfaces

We show that any stable hypersurface of a symplectic $4$-manifold, on which the cohomology class of the symplectic form restricts to a multiple of a rational class, can be $C^\infty$-approximated by (possibly unstable) hypersurfaces whose closed characteristics equidistribute. The cohomological condition is necessary due to a famous example of Herman. The proof combines KAM theory with recent quantitative closing lemmas for Reeb flows and area-preserving maps. As a further application, we prove that every geodesible volume-preserving vector field on a closed three-manifold can be $C^\infty$-approximated by volume-preserving vector fields with equidistributed periodic orbits.

math.SG↗