1,091 research outputs found
A new estimation method for mass of an isolated neutron star using gravitational waves
We investigate a possibility of estimating mass of an isolated rapidly
rotating neutron star (NS) from a continuous gravitational wave (GW) signal
emitted by the NS. When the GW passes through the gravitational potential of
the NS, the GW takes a slightly longer time to travel to an observer than it
does in the absence of the NS. Such a time dilation effect holds also for
photons and is often referred to as the gravitational time delay (or the
Shapiro time delay). Correspondingly, the phase of the GW from the NS shifts
due to the Coulomb type gravitational potential of the NS, and the resulting
logarithmic phase shift depends on the mass, the spin frequency of the NS, and
the distance to the NS. We show that the NS mass can, in principle, be obtained
by making use of the phase shift difference between two modes of the continuous
GW such as once and twice spin frequency modes induced by a freely precessing
NS or a NS containing a pinned superfluid core. We estimate the measurement
accuracy of the NS mass using Monte Carlo simulations and find that the mass of
the NS with its ellipticity at 1 kpc is typically measurable with an
accuracy using Einstein Telescope.Comment: 9 pages, 2 figure
Anchored Lagrangian submanifolds and their Floer theory
We introduce the notion of (graded) anchored Lagrangian submanifolds and use
it to study the filtration of Floer' s chain complex. We then obtain an
anchored version of Lagrangian Floer homology and its (higher) product
structures. They are somewhat different from the more standard non-anchored
version. The anchored version discussed in this paper is more naturally related
to the variational picture of Lagrangian Floer theory and so to the likes of
spectral invariants. We also discuss rationality of Lagrangian submanifold and
reduction of the coefficient ring of Lagrangian Floer cohomology of thereof.Comment: 40 page
Kuranishi structure, Pseudo-holomorphic curve, and virtual fundamental chain: Part 2
This article is the second part of the article we promised to write at the
end of Section 1 of [FOOO15] (arXiv:1209.4410). (Part I appeared in [Part I]
(arXiv:1503.07631).) We discuss the foundation of the virtual fundamental chain
and cycle technique, especially its version that appeared in [FOn] and also in
Section A1, Section 7.5 [FOOO4], Section 12 [FOOO7], [Fu2]. This article is
independent of our earlier writing [FOOO15]. We also do not assume that the
readers have any knowledge on the pseudo-holomorphic curve. In this second
part, we consider a system of spaces with Kuranishi structures (abbreviated as
a K-system) and its simultaneous perturbations.Comment: 277 pages, many figures, content index include
Exponential decay estimates and smoothness of the moduli space of pseudoholomorphic curves
In this paper, we examine the dependence of standard gluing process for
pseudoholomorphic curves under the change of the length of the neck-region
with respect to the cylindrical metrics associated to the given analytic
coordinates near the punctures in the setting of bordered open Riemann surface
with boundary punctures. We establish exponential decay of the -derivatives
of the -dependent family of glued solutions under the change of the length
of the neck-region in a precise manner. This exponential decay estimate is
an important ingredient to prove the smoothness of the Kuranishi structure
constructed on the compactified moduli space of pseudoholomorphic curves given
in the appendix of the authors' book. We also demonstrate the way how this
smoothness follows from the exponential decay.Comment: 111 pages, 17 figure
Lagrangian Floer theory over integers: spherically positive symplectic manifolds
In this paper we study the Lagrangian Floer theory over or . Under
an appropriate assumption on ambient symplectic manifold, we show that the
whole story of Lagrangian Floer theory in \cite{fooo-book} can be developed
over coefficients, and over coefficients when Lagrangian
submanifolds are relatively spin. The main technical tools used for the
construction are the notion of the sheaf of groups, and stratification and
compatibility of the normal cones applied to the Kuranishi structure of the
moduli space of pseudo-holomorphic discs.Comment: 68 pages; 4 figures; v2) 72 pages, to appearin the special issue of
Pure and Applied Mathematics Quarterly dedicated to Denis Sullivan's 70th
birthda
Displacement of polydisks and Lagrangian Floer theory
There are two purposes of the present article. One is to correct an error in
the proof of Theorem 6.1.25 in \cite{fooo:book}, from which Theorem J
\cite{fooo:book} follows. In the course of doing so, we also obtain a new lower
bound of the displacement energy of polydisks in general dimension. The results
of the present article are motivated by the recent preprint of Hind \cite{hind}
where the 4 dimensional case is studied. Our proof is different from Hind's
even in the 4 dimensional case and provides stronger result, and relies on the
study of torsion thresholds of Floer cohomology of Lagrangian torus fiber in
simple toric manifolds associated to the polydisks.Comment: 28 page
Lagrangian Floer theory and mirror symmetry on compact toric manifolds
In this paper we study Lagrangian Floer theory on toric manifolds from the
point of view of mirror symmetry. We construct a natural isomorphism between
the Frobenius manifold structures of the (big) quantum cohomology of the toric
manifold and of Saito's theory of singularities of the potential function
constructed in \cite{fooo09} via the Floer cohomology deformed by ambient
cycles. Our proof of the isomorphism involves the open-closed Gromov-Witten
theory of one-loop.Comment: 292 pages, 23 figures; final version in Asterisque, vol 376, 2016,
Societe Mathematique de Franc
Technical details on Kuranishi structure and virtual fundamental chain
This is an expository article on the theory of Kuranishi structure and is
based on a series of pdf files we uploaded for the discussion of the google
group named `Kuranishi' (with its administrator H. Hofer). There we replied to
several questions concerning Kuranishi structure raised by K. Wehrheim. At this
stage we submit this article to the e-print arXiv, all the questions or
objections asked in that google group were answered, supplemented or confuted
by us. We first discuss the abstract theory of Kuranishi structure and virtual
fundamental chain/cycle. This part can be read independently from other parts.
We then describe the construction of Kuranishi structure on the moduli space of
pseudoholomorphic curves, including the complete analytic detail of the gluing
construction as well as the smoothness of the resulting Kuranishi structure.
The case of S^1 equivariant Kuranishi structure which appears in the study of
time independent Hamiltonian and the moduli space of Floer's equation is
included.Comment: 257 pages. arXiv admin note: substantial text overlap with
arXiv:1208.1340 by other author
Kuranishi structure, Pseudo-holomorphic curve, and Virtual fundamental chain: Part 1
This is the first part of the article we promised at the end of [FOOO13,
Section 1]. We discuss the foundation of the virtual fundamental chain and
cycle technique, especially its version appeared in [FOn] and also in [FOOO4,
Section A1, Section 7.5], [FOOO7, Section 12], [Fu2]. In Part 1, we focus on
the construction of the virtual fundamental chain on a single space with
Kuranishi structure. We mainly discuss the de Rham version and so work over
-coefficients, but we also include a self-contained account of the
way how to work over -coefficients in case the dimension of the
space with Kuranishi structure is .
Part 1 of this document is independent of our earlier writing [FOOO13]. We
also do not assume the reader have any knowledge on the pseudo-holomorphic
curve, in Part 1.
Part 2 (resp. Part 3), which will appear in the near future, discusses the
case of a system of Kuranishi structures and its simultaneous perturbations
(resp. the way to implement the abstract story in the study of moduli spaces of
pseudo-holomorphic curves).Comment: 203 pages, contentindex include
Lagrangian Floer theory on compact toric manifolds: survey
This article is a survey of a series of papers [FOOO3,FOOO4,FOOO5] in which
we developed the method of calculation of Floer cohomology of Lagrangian torus
orbits in compact toric manifolds, and its applications to symplectic topology
and to mirror symmetry. In this article we summarize the main ingredients of
calculation and illustrate them by examples. The second half of the survey is
devoted to discussion of the most recent result from [FOOO5] (arXiv:1009.1648)
where the mirror symmetry between the two Frobenius manifolds arising from the
big quantum cohomology and from the K. Saito theory of singularities was
established.Comment: 60 pages, 5 figure
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