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Indexed by:期刊论文

Date of Publication:2009-02-01

Journal:JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS

Included Journals:SCIE

Volume:18

Issue:2

Page Number:199-208

ISSN No.:0218-2165

Key Words:Essential annuli; handlebody; maximal collection; annulus-busting curve

Abstract:It is known that a maximal collection of essential annuli in H(2) could contain exactly 1, or 2, or at most 3 annuli, and a maximal collection of essential annuli in H(n) with n >= 3 can contains at most 4n-5 annuli, and the bound is best possible. In the present paper, we show that a maximal collection of essential annuli in H(n) with n >= 3 contains at least two annuli, and for each m, 2 <= m <= 4n-5, there exists a maximal collection of essential annuli in H(n) which contains exactly m annuli.