Taesu Kim

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20192026

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math.SG2026

Kuranishi chart categories and higher cocycle conditions

Taesu Kim

Given an $L_{\infty}$ -Kuranishi space introduced in \cite{Kim1}, we propose a notion called the Kuranishi chart category. Using the nerve of this category, together with a choice of…

math.SG2026

Categorical structures of Kuranishi spaces with $L_{\infty} [1]$ -algebras

Taesu Kim

We introduce $L_{\infty}$ -Kuranishi spaces by associating, to each chart, $L_{\infty} [1]$ -algebras defined on open neighborhoods of points in the zero locus of the Kuranishi sectio…

math.SG2026

Stratifications associated to generic closed two-forms and stratified $L_{\infty}$ spaces

Taesu Kim, Yong-Geun Oh

Jae-Suk Park and the second-named author introduce the deformation problem of coisotropic submanifolds of a symplectic manifold as the study of Mauer-Cartan moduli problem of an $L…

math.SG2025

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

Taesu Kim

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 o…

math.SG2023

Analysis of pseudoholomorphic curves on symplectization: Revisit via contact instantons

Yong-Geun Oh, Taesu Kim

In this survey article, we present the analysis of pseudoholomorphic curves $u : (Σ ˙, j) \to (Q \times R, J)$ on the symplectization of contact manifold $(Q,λ)…

math.SG2023

Perturbation theory of asymptotic operators of contact instantons and pseudoholomorphic curves on symplectization

Taesu Kim, Yong-Geun Oh

In this paper, we first provide precise tensorial formulae for the asymptotic operators of contact instantons $w : Σ ˙ \to Q$ and of pseudoholomorphic curves $u:(\dotΣ,j) \to (Q \t…

Kuranishi chart categories and higher cocycle conditions

Categorical structures of Kuranishi spaces with L∞​[1]-algebras

Stratifications associated to generic closed two-forms and stratified L∞​ spaces

L∞​-Kuranishi spaces and the moduli space of pseudoholomorphic disks

Analysis of pseudoholomorphic curves on symplectization: Revisit via contact instantons

Perturbation theory of asymptotic operators of contact instantons and pseudoholomorphic curves on symplectization

Categorical structures of Kuranishi spaces with $L_{\infty} [1]$ -algebras

Stratifications associated to generic closed two-forms and stratified $L_{\infty}$ spaces

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