Release Time:2019-03-09  Hits:

Indexed by: Journal Article

Date of Publication: 2014-04-01

Journal: SCIENCE CHINA-MATHEMATICS

Included Journals: SCIE

Volume: 57

Issue: 4

Page Number: 847-854

ISSN: 1674-7283

Key Words: curve complex; connectedness; i-distance; surface

Abstract: For a closed orientable surface S (g) of genus not smaller than 2, C(S (g) ) is the curve complex on S (g) whose vertices consist of the isotopy classes of nontrivial circles on S (g) . It has been showed that any two vertices in C(S (g) ) can be connected by an edge path, and C(S (g) ) has an infinite diameter. We show that for 0 a (c) 1/2 i a (c) 1/2 3g-5, two i-simplices can be connected by an (i +1)-path in C(S (g) ), and the diameter of C(S (g) ) under such a distance is infinite.