The conformal module of conjugacy classes braids is an invariant that appeared earlier than the entropy braids, and inversely proportional to entropy. Using relation between two invariants, we give a short conceptional proof result on module. Mainly, consider situations, when serves as obstruction for existence homotopies (or isotopies) smooth objects involving respective holomorphic objects, p...

We examine the Kerr/CFT correspondence in Einstein gravity extended with quadratic curvature invariants. consider two explicit examples four and five dimensions compute central charges of asymptotic symmetry algebras near horizon geometries, using improved version BBC formalism that encompasses information Lagrangian. find resulting Cardy entropy differs from Wald entropy, caused by Riemann-squ...

We study slow entropy invariants for abelian unipotent actions $ U on any finite volume homogeneous space G/\Gamma $. For every such action we show that the topological can be computed directly from dimension of a special decomposition {{\rm{Lie}}}(G) induced by {{\rm{Lie}}}(U) Moreover, are able to metric coincides with its entropy. As corollary, obtain complexity horocyclic is only related G ...

We review and elaborate on certain aspects of the connections between instanton counting in maximally supersymmetric gauge theories and the computation of enumerative invariants of smooth varieties. We study in detail three instances of gauge theories in six, four, and two dimensions which naturally arise in the context of topological string theory on certain noncompact threefolds. We describe ...

We show why the amount of information communicated between the past and future-the excess entropy-is not in general the amount of information stored in the present-the statistical complexity. This is a puzzle, and a long-standing one, since the former describes observed behavior, while optimal prediction requires the latter. We present a closed-form expression for the excess entropy in terms of...

In this paper we propose a methodology based on Topogical Data Analysis (TDA) for capturing when a complex system, represented by a multivariate time series, changes its internal organization. The modification of the inner organization among the entities belonging to a complex system can induce a phase transition of the entire system. In order to identify these reorganizations, we designed a ne...

certain algebraic invariants of the integral group ring zg of a group g were introduced and investigated in relation to the problem of extending the farrell-tate cohomology, which is defined for the class of groups of finite virtual cohomological dimension. it turns out that the finiteness of these invariants of a group g implies the existence of a generalized farrell-tate cohomology for g whic...

We review recent results in the study of regular four dimensional BPS black holes in toroidally compactified type II (or M) theory. We discuss the generating solution for this kind of black holes, its microscopic description(s), and compute the corresponding microscopic entropy. These achievements, which provide a description of the fundamental degrees of freedom accounting for the entropy of a...