Homotopy models for $L_{\infty}[1]$-algebras in higher degrees

Taesu Kim

Homotopy models for $L_{\infty}[1]$-algebras in higher degrees

Algebraic Topology 2026-06-27 v1 Quantum Algebra Symplectic Geometry

Authors: Taesu Kim

Abstract

We propose a model of higher homotopy theory of $L_{\infty}[1]$ -morphisms as a natural generalization of the $A_{\infty}$ -homotopies defined by Fukaya-Oh-Ohta-Ono \cite{FOOO1}. Within this framework, we show that a filling condition holds for simplices whose vertices are assigned quasi-isomorphisms.

Keywords

L-infinity algebra homotopy theory A-infinity homotopy quasi-isomorphism filling condition higher homotopy

Cite

@article{arxiv.2606.28985,
  title  = {Homotopy models for $L_{\infty}[1]$-algebras in higher degrees},
  author = {Taesu Kim},
  journal= {arXiv preprint arXiv:2606.28985},
  year   = {2026}
}

Comments

22 pages. A reformatted version as an independent preprint from arXiv:2511.05206v1, focusing on Part I (Homological Algebra)