Elements of Morse theory on Aleksandrov spaces. (English. Russian original) Zbl 0815.53072

St. Petersbg. Math. J. 5, No. 1, 205-213 (1994); translation from Algebra Anal. 5, No. 1, 232-241 (1993).
Summary: We present a version of elementary Morse theory for distance functions on an Aleksandrov space with curvature bounded from below. It is proved that 1) any small spherical neighborhood of a point in an Aleksandrov space is homeomorphic to the open cone over its boundary, and 2) any Aleksandrov space admits a canonical stratification whose strata are topological manifolds.


53C45 Global surface theory (convex surfaces à la A. D. Aleksandrov)
57Q99 PL-topology