JournalsjemsOnline First25 January 2022

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

  • Jiayin Pan

    University of California, Santa Barbara, USA; The Fields Institute for Research in Mathematical Sciences, Toronto, Canad
  • Guofang Wei

    University of California, Santa Barbara, USA
Semi-local simple connectedness of non-collapsing Ricci limit spaces cover
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Abstract

Let XX be a non-collapsing Ricci limit space and let xXx\in X. We show that for any ϵ>0\epsilon>0, there is r>0r>0 such that every loop in Bt(x)B_t(x) is contractible in B(1+ϵ)t(x)B_{(1+\epsilon)t}(x), where t(0,r]t\in(0,r]. In particular, XX is semi-locally simply connected.

Cite this article

Jiayin Pan, Guofang Wei, Semi-local simple connectedness of non-collapsing Ricci limit spaces. J. Eur. Math. Soc. (2022), published online first

DOI 10.4171/JEMS/1166