569 research outputs found
Of Sullivan models, Massey products, and twisted Pontrjagin products
Associated to every connected, topological space there is a Hopf algebra
- the Pontrjagin ring of the based loop space of the configuration space of two
points in X. We prove that this Hopf algebra is not a homotopy invariant of the
space. We also exhibit interesting examples of H-spaces, which are homotopy
equivalent as spaces, which either lead to isomorphic rational Hopf algebras or
not, depending crucially on the existence of Whitehead products. Moreover, we
investigate a (naturally motivated) twisted version of these Pontrjagin rings
in the various aforementioned contexts. In all of these examples, Massey
products abound and play a key role.Comment: 27 pages, 2 figures; made minor changes in abstract and proposition
Homotopy groups of highly connected manifolds
In this paper we give a formula for the homotopy groups of -connected
-manifolds as a direct sum of homotopy groups of spheres in the case the
Betti number is larger than . We demonstrate that when the
Betti number is the homotopy groups might not have such a decomposition.
The techniques used in this computation also yield formulae for homotopy groups
of connected sums of sphere products and CW complexes of a similar type. In all
the families of spaces considered here, we establish a conjecture of J. C.
Moore
Homotopy groups of certain highly connected manifolds via loop space homology
For we consider -connected closed manifolds of dimension at
most . We prove that away from a finite set of primes, the -local
homotopy groups of are determined by the dimension of the space of
indecomposable elements in the cohomology ring . Moreover, we show
that these -local homotopy groups can be expressed as direct sum of
-local homotopy groups of spheres. This generalizes some of the results of
our earlier work
On the cohomology ring and upper characteristic rank of Grassmannian of oriented -planes
In this paper we study the mod cohomology ring of the Grasmannian
of oriented -planes in . We determine
the degrees of the indecomposable elements in the cohomology ring. We also
obtain an almost complete description of the cohomology ring. This partial
description allows us to provide lower and upper bounds on the cup length of
. As another application, we show that the upper
characteristic rank of equals the characteristic rank of
, the oriented tautological bundle over
.Comment: 23 page
Enumeration of curves with one singular point
In this paper we obtain an explicit formula for the number of degree d curves
in two dimensional complex projective space, passing through (d(d+3)/2 -k)
generic points and having a codimension k singularity, where k is at most 7. In
the past, many of these numbers were computed using techniques from algebraic
geometry. In this paper we use purely topological methods to count curves. Our
main tool is a classical fact from differential topology: the number of zeros
of a generic smooth section of a vector bundle V over M, counted with a sign,
is the Euler class of V evaluated on the fundamental class of M.Comment: 61 pages; changed to larger version (this one) to facilitate
reference regarding detail
Counting curves on a general linear system with up to two singular points
In this paper we obtain an explicit formula for the number of curves in a
compact complex surface (passing through the right number of generic
points), that has up to one node and one singularity of codimension ,
provided the total codimension is at most . We use a classical fact from
differential topology: the number of zeros of a generic smooth section of a
vector bundle over , counted with signs, is the Euler class of
evaluated on the fundamental class of .Comment: 22 pages; generalizes results of our previous papers to curves on any
linear system. We welcome comments and suggestion
Nambu Structures And Associated Bialgebroids
This paper investigates higher order generalizations of well known results
for Lie algebroids and bialgebroids. It is proved that -Lie algebroid
structures correspond to -ary generalization of Gerstenhaber algebras and
are implied by -ary generalization of linear Poisson structures on the dual
bundle. A Nambu-Poisson manifold (of order ) gives rise to a special
bialgebroid structure which is referred to as a weak Lie-Filippov bialgebroid
(of order ). It is further demonstrated that such bialgebroids canonically
induce a Nambu-Poisson structure on the base manifold. Finally, the tangent
space of a Nambu Lie group gives an example of a weak Lie-Filippov bialgebroid
over a point.Comment: Final version, 33 Page
Homotopy groups and periodic geodesics of closed 4-manifolds
Given a simply connected, closed four manifold, we associate to it a simply
connected, closed, spin five manifold. This leads to several consequences : the
stable and unstable homotopy groups of such a four manifold is determined by
its second Betti number, and the ranks of the homotopy groups can be explicitly
calculated. We show that for a generic metric on such a smooth four manifold
with second Betti number at least three, the number of geometrically distinct
periodic geodesics of length at most l grow exponentially as a function of l.
The number of closed Reeb orbits of length at most l on the spherization of the
cotangent bundle also grow exponentially for any Reeb flow.Comment: 24 pages; added a result on closed Reeb orbit
Core-crust transition and crustal fraction of moment of inertia in neutron stars
The crustal fraction of moment of inertia in neutron stars is calculated
using -equilibrated nuclear matter obtained from density dependent M3Y
effective interaction. The transition density, pressure and proton fraction at
the inner edge separating the liquid core from the solid crust of the neutron
stars determined from the thermodynamic stability conditions are found to be
0.0938 fm, P 0.5006 MeV fm and 0.0308,
respectively. The crustal fraction of the moment of inertia can be extracted
from studying pulsar glitches and is most sensitive to the pressure as well as
density at the transition from the crust to the core. These results for
pressure and density at core-crust transition together with the observed
minimum crustal fraction of the total moment of inertia provide a new limit for
the radius of the Vela pulsar: kms.Comment: 6 pages including 2 figures and 3 tables; Calculations are made more
accurate by using very accurate values of Solar mass, erg to MeV conversion
factor, pi and gravitational constant G. arXiv admin note: substantial text
overlap with arXiv:1406.5302; text overlap with arXiv:hep-ph/0009357,
arXiv:hep-ph/0011333, arXiv:hep-ph/0109135, arXiv:hep-ph/0102047 by other
author
Landau quantization and mass-radius relation of magnetized White Dwarfs in general relativity
Recently, several white dwarfs have been proposed with masses significantly
above the Chandrasekhar limit, known as Super-Chandrasekhar White Dwarfs, to
account for the overluminous Type Ia supernovae. In the present work, Equation
of State of a completely degenerate relativistic electron gas in magnetic field
based on Landau quantization of charged particles in a magnetic field is
developed. The mass-radius relations for magnetized White Dwarfs are obtained
by solving the Tolman-Oppenheimer-Volkoff equations. The effects of the
magnetic energy density and pressure contributed by a density-dependent
magnetic field are treated properly to find the stability configurations of
realistic magnetic White Dwarf stars.Comment: 8 pages including 4 Tables & 4 figures; Typographical error of
Eqn.(29) is corrected and 3 new Refs. added in this versio
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