Release Time:2019-03-09  Hits:

Indexed by: Journal Article

Date of Publication: 2011-12-01

Journal: JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS

Included Journals: SCIE、Scopus

Volume: 20

Issue: 12

Page Number: 1709-1721

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 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).