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Indexed by:期刊论文

Date of Publication:2014-04-01

Journal:SCIENCE CHINA-MATHEMATICS

Included Journals:SCIE

Volume:57

Issue:4

Page Number:847-854

ISSN No.: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.