23 research outputs found
Constructing Seifert surfaces from n-bridge link projections
This paper presents a new algorithm "A" for constructing Seifert surfaces
from n-bridge projections of links. The algorithm produces minimal complexity
surfaces for large classes of braids and alternating links. In addition, we
consider a family of knots for which the canonical genus is strictly greater
than the genus, (g_c(K) > g(K)), and show that A builds surfaces realizing the
knot genus g(K). We also present a generalization of Seifert's algorithm which
may be used to construct surfaces representing arbitrary relative second
homology classes in a link complement.Comment: 19 pages, 15 figure
Asymmetric hyperbolic L-spaces, Heegaard genus, and Dehn filling
An L-space is a rational homology 3-sphere with minimal Heegaard Floer
homology. We give the first examples of hyperbolic L-spaces with no symmetries.
In particular, unlike all previously known L-spaces, these manifolds are not
double branched covers of links in S^3. We prove the existence of infinitely
many such examples (in several distinct families) using a mix of hyperbolic
geometry, Floer theory, and verified computer calculations. Of independent
interest is our technique for using interval arithmetic to certify symmetry
groups and non-existence of isometries of cusped hyperbolic 3-manifolds. In the
process, we give examples of 1-cusped hyperbolic 3-manifolds of Heegaard genus
3 with two distinct lens space fillings. These are the first examples where
multiple Dehn fillings drop the Heegaard genus by more than one, which answers
a question of Gordon.Comment: 19 pages, 2 figures. v2: minor changes to intro. v3: accepted
version, to appear in Math. Res. Letter
A User's Guide to Morse Foliated Open Books
Morse foliated open books were introduced by the autors (along with abstract
and embedded versions) as a tool for studying contact manifolds with boundary,
and this article illustrates the advantages of the Morse perspective. We use
this to extend the definition of \textit{right-veering} to foliated open books
and we show that it plays a similar role in detecting overtwistedness as in
other versions of open books.Comment: 16 pages, 12 picture