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arXiv · 2108.11030

Collapsing to Alexandrov spaces with isolated mild singularities

Tadashi Fujioka
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Abstract

Let $M_j$ be a sequence of Riemannian manifolds with sectional curvature bound below collapsing to a compact Alexandrov space $X$ of dimension $k$. Suppose that all but finitely many points of $X$ are $(k,\delta)$-strained and that the space of directions at each exceptional point contains $k+1$ directions making obtuse angles with each other. We prove that $M_j$ admits a structure of locally trivial fibration over $X$ for sufficiently large $j$. The same is true for collapsing sequences of Alexandrov spaces such that the infimum of the volume of the spaces of directions is sufficiently large relative to $\delta$.

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Tadashi Fujioka. 2021-08-25. Collapsing to Alexandrov spaces with isolated mild singularities. https://doi.org/10.1016/j.difgeo.2022.101951

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