Release Time:2019-03-10  Hits:

Indexed by: Journal Article

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: 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.