Cohomological invariants of a variation of flat connection

In this paper, we apply the theory of Chern-Cheeger-Simons to construct canonical invariants associated to a $r$-simplex whose points parametrize flat connections on a smooth manifold $X$. These invariants lie in degrees $(2p-r-1)$-cohomology with $C/Z$-coefficients, for $p> r\geq 1$. In turn, this corresponds to a homomorphism on the higher homology groups of the moduli space of flat connections, and taking values in $C/Z$-cohomology of the underlying smooth manifold $X$.Comment: 15 p. Final version, to appear. arXiv admin note: text overlap with arXiv:1310.000

The Chern character of a parabolic bundle, and a parabolic Reznikov theorem in the case of finite order at infinity

In this paper, we obtain an explicit formula for the Chern character of a locally abelian parabolic bundle in terms of its constituent bundles. Several features and variants of parabolic structures are discussed. Parabolic bundles arising from logarithmic connections form an important class of examples. As an application, we consider the situation when the local monodromies are semi-simple and are of finite order at infinity. In this case the parabolic Chern classes of the associated locally abelian parabolic bundle are deduced to be zero in the rational Deligne cohomology in degrees $\geq 2$.Comment: Adds and corrects reference

Quantum differential operators on the quantum plane

The universal enveloping algebra U(g) of a Lie algebra g acts on its representation ring R through D(R), the ring of differential operators on R. A quantised universal enveloping algebra (or "quantum group") is a deformation of a universal enveloping algebra and acts not through the differential operators of its representation ring but through the quantised differential operators of its representation ring. We present this situation for the quantum group of sl_2.Comment: 18 pages, references added, address change

Determination of mass of IGR J17091-3624 from "Spectro-Temporal" variations during onset-phase of the 2011 outburst

The 2011 outburst of the black hole candidate IGR J17091-3624 followed the canonical track of state transitions along with the evolution of Quasi-Periodic Oscillation (QPO) frequencies before it began exhibiting various variability classes similar to GRS 1915+105. We use this canonical evolution of spectral and temporal properties to determine the mass of IGR J17091-3624, using three different methods, viz : Photon Index ($\Gamma$) - QPO frequency ($\nu$) correlation, QPO frequency ($\nu$) - Time (day) evolution and broadband spectral modelling based on Two Component Advective Flow. We provide a combined mass estimate for the source using a Naive Bayes based joint likelihood approach. This gives a probable mass range of 11.8 M$_{\odot}$ - 13.7 M$_{\odot}$. Considering each individual estimate and taking the lowermost and uppermost bounds among all three methods, we get a mass range of 8.7 M$_{\odot}$ - 15.6 M$_{\odot}$ with 90% confidence. We discuss the probable implications of our findings in the context of two component accretion flow.Comment: 10 pages, 5 figures (4 in colour), 2 tables. Accepted for publication in Ap