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Semi-local simple connectedness of non-collapsing Ricci limit spaces

Authors :
Pan, Jiayin
Wei, Guofang
Publication Year :
2019

Abstract

Let $X$ be a non-collapsing Ricci limit space and let $x\in X$. We show that for any $\epsilon>0$, there is $r>0$ such that every loop in $B_t(x)$ is contractible in $B_{(1+\epsilon)t}(x)$, where $t\in(0,r]$. In particular, $X$ is semi-locally simply connected.<br />Comment: Slightly modified the proof of Theorem 3.5 to fix a minor error on local covers. Slightly modified the proofs of Lemmas 3.2, 3.6, and 3.8 to fix a minor error on estimating $\rho(t,x)$ by a nearby point. Fixed some typos

Details

Database :
arXiv
Publication Type :
Report
Accession number :
edsarx.1904.06877
Document Type :
Working Paper
Full Text :
https://doi.org/10.4171/JEMS/1166