@Article{JMS-58-3,
author = {Pan , Jiayin},
title = {Ricci Curvature and Fundamental Groups of Effective Regular Sets},
journal = {Journal of Mathematical Study},
year = {2025},
volume = {58},
number = {1},
pages = {3--21},
abstract = {<p style="text-align: justify;">For a Gromov-Hausdorff convergent sequence of closed manifolds $M^n_i\xrightarrow{GH} X$ with ${\rm Ric}\ge -(n-1)$, ${\rm diam}(M_i) ≤ D,$ and ${\rm vol}(M_i) ≥ v &gt; 0,$ we study the relation between $π_1(M_i)$ and $X.$ It was known before that there is a surjective homomorphism $ϕ_i
: π_1(M_i) → π_1(X)$ by the work of Pan-Wei. In this paper, we construct a surjective
homomorphism from the interior of the effective regular set in $X$ back to $M_i,$ that is, $ψ_i
:π_1(\mathcal{R}^◦_{ϵ,δ} )→π_1(M_i).$ These surjective homomorphisms $ϕ_i$ and $ψ_i$ are natural in the
sense that their composition $ϕ_i◦ψ_i$ is exactly the homomorphism induced by the inclusion map $R^◦_{ ϵ,δ}\hookrightarrow X.$</p>},
issn = {2617-8702},
doi = {https://doi.org/10.4208/jms.v58n1.25.01},
url = {http://global-sci.org/intro/article_detail/jms/23935.html}
}