13,480 research outputs found
Chart description for genus-two Lefschetz fibrations and a theorem on their stabilization
Chart descriptions are a graphic method to describe monodromy representations
of various topological objects. Here we introduce a chart description for
genus-two Lefschetz fibrations, and show that any genus-two Lefschetz fibration
can be stabilized by fiber-sum with certain basic Lefschetz fibrations.Comment: 17 pages, 18 figure
Span of the Jones polynomial of an alternating virtual link
For an oriented virtual link, L.H. Kauffman defined the f-polynomial (Jones
polynomial). The supporting genus of a virtual link diagram is the minimal
genus of a surface in which the diagram can be embedded. In this paper we show
that the span of the f-polynomial of an alternating virtual link L is
determined by the number of crossings of any alternating diagram of L and the
supporting genus of the diagram. It is a generalization of
Kauffman-Murasugi-Thistlethwaite's theorem. We also prove a similar result for
a virtual link diagram that is obtained from an alternating virtual link
diagram by virtualizing one real crossing. As a consequence, such a diagram is
not equivalent to a classical link diagram.Comment: Published by Algebraic and Geometric Topology at
http://www.maths.warwick.ac.uk/agt/AGTVol4/agt-4-46.abs.htm
On the strong coupling scale in Higgs G-inflation
Higgs G-inflation is an inflation model that takes advantage of a
Galileon-like derivative coupling. It is a non-renormalizable operator and is
strongly coupled at high energy scales. Perturbative analysis does not have a
predictive power any longer there. In general, when the Lagrangian is expanded
around the vacuum, the strong coupling scale is identified as the mass scale
that appears in non-renormalizable operators. In inflationary models, however,
the identification of the strong coupling scale is subtle, since the structures
of the kinetic term as well as the interaction itself can be modified by the
background inflationary dynamics. Therefore, the strong coupling scale depends
on the background. In this letter, we evaluate the strong coupling scale of the
fluctuations around the background in the Higgs G-inflation including the
Nambu-Goldstone modes associated with the symmetry breaking. We find that the
system is sufficiently weakly coupled when the scales which we now observe exit
the horizon during inflation and the observational predictions with the
semiclassical treatment are valid. However, we also find that the inflaton
field value at which the strong coupling scale and the Hubble scale meet is
less than the Planck scale. Therefore, we cannot describe the model from the
Planck scale, or the chaotic initial condition.Comment: 8 pages; v2: typos corrected, references added, matches version
published in PL
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