6 papers
Kwasik--Schultz manifolds are -compactifiable
Shijie Gu
Kwasik and Schultz constructed two-ended open -manifolds which satisfy the usual finiteness and stability conditions at infinity but do not admit arbitrarily small -neighborh…
Busemann G-spaces with convex balls
Tadashi Fujioka, Shijie Gu
We prove that any Busemann G-space such that every sufficiently small metric ball is convex is a topological manifold. The key ingredient in the proof is Ivanov's Helly theorem. Th…
Finsler structure of Busemann G-spaces
Tadashi Fujioka, Shijie Gu
We provide two sufficient conditions for a Busemann G-space to admit a differentiable DC atlas with a continuous Finsler metric, from the viewpoint of comparison geometry. These re…
Topological regularity of Busemann spaces of nonpositive curvature
Tadashi Fujioka, Shijie Gu
We extend the topological results of Lytchak-Nagano and Lytchak-Nagano-Stadler for CAT(0) spaces to the setting of Busemann spaces of nonpositive curvature, i.e., BNPC spaces. We g…
Nonembeddable contractible open manifolds arising from Whitehead doubling
Shijie Gu, Jian Wang, Yanqing Zou
We study a family of genus-one contractible open manifolds constructed by iterated Whitehead doubling from a nontrivial knot and an even half-twist . For each such pair, we…
On Z-compactifiability of manifolds
Shijie Gu
In 1976, Chapman and Siebenmann established necessary and sufficient conditions for -compactifying Hilbert cube manifolds. Although the corresponding conditions are known to be…