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Indexed by:期刊论文

Date of Publication:2011-12-01

Journal:JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS

Included Journals:Scopus、SCIE

Volume:20

Issue:12

Page Number:1709-1721

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 it is clear how they are embedded in H(2). It is also known that for a maximal collection A of essential annuli in H(n) with n >= 3, 2 <= vertical bar A vertical bar <= 4n - 5, and the bounds are sharp. Moreover, for each integer m, 2 <= m <= 4n - 5, there exists a maximal collection of essential annuli in H(n) which contains exactly m annuli. In this paper, we detect how a maximal collection of essential annuli in H(n) with n >= 3 are embedded in H(n).