1,820 research outputs found
Seifert surfaces in open books, and a new coding algorithm for links
We introduce a new standard form of a Seifert surface . In that standard
form, is obtained by successively plumbing flat annuli to a disk , where
the gluing regions are all in . We show that any link has a Seifert surface
in the standard form, and thereby present a new way of coding a link. We
present an algorithm to read the code directly from a braid presentation.Comment: 10 page
Branched covers of quasipositive links and L-spaces
Let be a oriented link such that , the -fold cyclic cover
of branched over , is an L-space for some . We show that if
either is a strongly quasipositive link other than one with Alexander
polynomial a multiple of , or is a quasipositive
link other than one with Alexander polynomial divisible by , then there is an integer , determined by the Alexander
polynomial of in the first case and the Alexander polynomial of and the
smooth -genus of , , in the second, such that . If
is a strongly quasipositive knot with monic Alexander polynomial such as an
L-space knot, we show that is not an L-space for , and
that the Alexander polynomial of is a non-trivial product of cyclotomic
polynomials if is an L-space for some . Our
results allow us to calculate the smooth and topological 4-ball genera of, for
instance, quasi-alternating quasipositive links. They also allow us to classify
strongly quasipositive alternating links and -strand pretzel links.Comment: 49 pages, 7 figures, minor corrections and improved exposition,
accepted for publication by the Journal of Topolog
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