相关论文: A remark on renormalized volume and Euler characte…

We obtain an analytic expression for the highly damped asymptotic quasinormal mode frequencies of the $d\geq 5$-dimensional Schwarzschild black hole modified by the Gauss-Bonnet term, which appears in string derived models of gravity. The…

Let $M$ be an oriented smooth manifold, and $\operatorname{Homeo}(M,\omega)$ the group of measure preserving homeomorphisms of $M$, where $\omega$ is a finite measure induced by a volume form. In this paper we define volume and Euler…

The squashed and stretched 7-dimensional internal metric preserving U(1) x U(1) x U(1)_R symmetry possesses an Einstein-Kahler 2-fold which is a base manifold of 5-dimensional Sasaki-Einstein L^{p, q, r} space. The r(transverse to the…

A topological version of a longstanding conjecture of H. Hopf, originally proposed by W. Thurston, states that the sign of the Euler characteristic of a closed aspherical manifold of dimension $d=2m$ depends only on the parity of $m$.…

These are lecture notes prepared for the summer school "Geometric, algebraic and topological methods in quantum field theory", held in Villa de Leyva in July 2017. Our goal is to provide an introduction to a conjecture of Chern that states…

This paper gives a way to renormalise certain quantum field theories on compact manifolds. Examples include Yang-Mills theory (in dimension 4 only), Chern-Simons theory and holomorphic Chern-Simons theory. The method is within the framework…

By studying the previously known holographic N=4 supersymmetric renormalization group flow(Gowdigere-Warner) in four dimensions, we find the mass deformed Chern-Simons matter theory which has N=4 supersymmetry by adding the four mass terms…

We study the critical points of the renormalized volume for acylindrical geometrically finite hyperbolic 3-manifolds that include rank-1 cusps, and show that the renormalized volume is locally convex around these critical points. We give a…

In this work a relation between topology and thermodynamical features of gravitational instantons is shown. The expression for the Euler characteristic, through the Gauss-Bonnet integral, and the one for the entropy of gravitational…

A (3+1)-dimensional Einstein-Gauss-Bonnet effective description of gravity has been recently formulated as the $D \to 4$ limit of the higher dimensional field equations after the rescaling of the coupling constant. This approach has been…

The hyperbolic structure on a 3-dimensional cone-manifold with a knot as singularity can often be deformed into a limiting Euclidean structure. In the present paper we show that the respective normalised Euclidean volume is always an…

Models of gravity with variable G and Lambda have acquired greater relevance after the recent evidence in favour of the Einstein theory being nonperturbatively renormalizable in the Weinberg sense. The present paper applies the…

We produce some explicit examples of conformally compact Einstein manifolds, whose conformal compactifications are foliated by Riemannian products of a closed Einstein manifold with the total space of a principal circle bundle over products…

Let {(M,g_i)} be a sequence of smooth compact oriented Einstein 4-manifolds of fixed Einstein constant $\lambda > 0$ that Gromov-Hausdorff converges to a 4-dimensional Einstein orbifold X. Suppose, moreover, that the limit metric is…

Einstein-Maxwell-Gauss-Bonnet-axion theory in $4$-dimensional spacetime is investigated in this paper through a "Kaluza-Klein-like" process. Dual to systems at finite temperature with background magnetic field on three dimensions, the…

We develop a general procedure, based on the renormalized eta-cochain, which allows to find local representatives of the bivariant Chern character of finitely summable quasihomomorphisms. In particular, using zeta-function renormalization…

We study the volume of compact Riemannian manifolds which are Einstein with respect to a metric connection with (parallel) skew-torsion. We provide a result for the sign of the first variation of the volume in terms of the corresponding…

A new framework to perturbative quantum gravity is proposed following the geometry of nonholonomic distributions on (pseudo) Riemannian manifolds. There are considered such distributions and adapted connections, also completely defined by a…

We study cosmological solutions of Einstein gravity with a positive cosmological constant in diverse dimensions. These include big-bang models that re-collapse, big-bang models that approach de Sitter acceleration at late times, and bounce…

We give lower bounds, in terms of the Euler characteristic, for the $L^2$-norm of the Weyl curvature of closed Riemannian 4-manifolds. The same bounds were obtained by Gursky, in the case of positive scalar curvature metrics.