1,570 research outputs found
Internal Quasiperiod Queries
Internal pattern matching requires one to answer queries about factors of a
given string. Many results are known on answering internal period queries,
asking for the periods of a given factor. In this paper we investigate (for the
first time) internal queries asking for covers (also known as quasiperiods) of
a given factor. We propose a data structure that answers such queries in
time for the shortest cover and in time for a representation of all the covers, after time
and space preprocessing.Comment: To appear in the SPIRE 2020 proceeding
Mutations and short geodesics in hyperbolic 3-manifolds
In this paper, we explicitly construct large classes of incommensurable
hyperbolic knot complements with the same volume and the same initial (complex)
length spectrum. Furthermore, we show that these knot complements are the only
knot complements in their respective commensurabiltiy classes by analyzing
their cusp shapes.
The knot complements in each class differ by a topological cut-and-paste
operation known as mutation. Ruberman has shown that mutations of hyperelliptic
surfaces inside hyperbolic 3-manifolds preserve volume. Here, we provide
geometric and topological conditions under which such mutations also preserve
the initial (complex) length spectrum. This work requires us to analyze when
least area surfaces could intersect short geodesics in a hyperbolic 3-manifold.Comment: This is the final (accepted) version of this pape
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