A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Extends Penrose's method to null shells with pressure and energy flux.
A new spectrum recovers cobordism cut and paste groups of manifolds with boundary.
In this paper, we shall be concerned with a relation between TQFTs and cut and paste invariants introduced by Karras, Kreck, Neumann and Ossa. Cut and paste invariants, or SK invariants, are functions on the set of smooth manifolds that are invariant under the cutting and pasting operation. Central to the work in this …
A simple method to create new 4-manifolds by altering fundamental groups.
In this note we study the relative Kervaire semi-characteristic and prove its invariance under cut-and-past operation. Our approach is analytic and follow very closely the method introduced by W. Zhang
We discuss the behaviour of the signature index class of closed foliated bundles under the operation of cutting and pasting. Along the way we establish several index theoretic results: we define Atiyah-Patodi-Singer (APS) index classes for Dirac-type operators on foliated bundles with boundary; we prove a relative inde…
Recent work of Jonathan Campbell and Inna Zakharevich has focused on building machinery for studying scissors congruence problems via algebraic -theory, and applying these tools to studying the Grothendieck ring of varieties. In this paper we give a new application of their framework: we construct a -space that r…
These are lecture notes on cut-and-paste methods in 3-dimensional contact geometry.
Counterexample disproves recent Penrose conjecture variant.
Constructs homologies for ribbon graphs to recover Penrose polynomials.
In this paper, we will introduce a cut and paste move, called a geometrically null log transform, and prove that any two manifolds related by a sequence of these moves become diffeomorphic afte r one stabilization. To motivate the cut and paste move, we will use the symplec tic fiber sum, and a construction of Fintushe…
New relations for Penrose polynomial at n=4 and n=3.
Study how past eon's matter affects present eon in Penrose's cyclic cosmology.
Schwarzschild 3-manifold stability proven for 3D Penrose inequality.
Smooth metrics satisfying Penrose inequality are necessarily smooth.
We investigate the Penrose limits of classical string and M-theory backgrounds. We prove that the number of (super)symmetries of a supergravity background never decreases in the limit. We classify all the possible Penrose limits of AdS x S spacetimes and of supergravity brane solutions. We also present the Penrose limi…
Extends Penrose limit to Finsler spacetimes.
Penrose limit results for specific 3-surfaces in space-time.
Throughout the literature on the charged Riemannian Penrose inequality, it is generally assumed that there is no charged matter present; that is, the electric field is divergence-free. The aim of this article is to clarify when the charged Riemannian Penrose inequality holds in the presence of charged matter, and when …
Paper applies Newman-Penrose formalism to ACM manifolds.
New proof of Penrose inequality using potential theory.
Conditions for Penrose-Ward transformation on specific manifolds.
We propose a geometric inequality for two-dimensional spacelike surfaces in the Schwarzschild spacetime. This inequality implies the Penrose inequality for collapsing dust shells in general relativity, as proposed by Penrose and Gibbons. We prove that the inequality holds in several important cases.
New classification of nonorientable 4-manifolds with specific fundamental groups.
The null Penrose inequality, i.e. the Penrose inequality in terms of the Bondi energy, is studied by introducing a funtional on surfaces and studying its properties along a null hypersurface extending to past null infinity. We prove a general Penrose-type inequality which involves the limit at infinity of the Hawki…
The purpose of this article is to view the Penrose kite from the perspective of symplectic geometry.
Proves existence of solutions to Einstein constraints with specific boundary conditions and verifies Penrose inequality.
The conformal flow of metrics [2] has been used to successfully establish a special case of the Penrose inequality, which yields a lower bound for the total mass of a spacetime in terms of horizon area. Here we show how to adapt the conformal flow of metrics, so that it may be applied to the Penrose inequality for gene…
Establishes a Penrose-type inequality for static spacetimes.
The Penrose-Kauffman polynomial connects knot theory to graph coloring.
The paper calculates Veech groups and Galois invariants for general origamis.
Study rigidity in Penrose's singularity theorem with weakly trapped surfaces.
We establish versions of the Positive Mass and Penrose inequalities for a class of asymptotically hyperbolic hypersurfaces. In particular, under the usual dominant energy condition, we prove in all dimensions an optimal Penrose inequality for certain graphs in hyperbolic space whose boundary…
Proves Penrose inequality in all dimensions for specific manifolds.
Various complexes of differential operators are constructed on complex projective space via the Penrose transform, which also computes their cohomology.
Proves Riemannian Penrose Inequality for specific manifolds.
We prove that the Penrose limit of a spacetime along a homogeneous geodesic is a homogeneous plane wave spacetime and that the Penrose limit of a reductive homogeneous spacetime along a homogeneous geodesic is a Cahen--Wallach space. We then consider several homogenous examples to show that these results are indeed sha…
In arXiv:0905.2622v1 and arXiv:0910.4785v1, Bray and Khuri outlined an approach to prove the Penrose inequality for general initial data sets of the Einstein equations. In this paper we extend this approach so that it may be applied to a charged version of the Penrose inequality. Moreover, assuming that the initial dat…
Study Penrose inequality for metrics with singular sets.
We point out that algebraically special Einstein fields with twisting rays exhibit the basic properties of conformal Universes considered recently by Roger Penrose.
The Penrose inequality gives a lower bound for the total mass of a spacetime in terms of the area of suitable surfaces that represent black holes. Its validity is supported by the cosmic censorship conjecture and therefore its proof (or disproof) is an important problem in relation with gravitational collapse. The Penr…
The Riemannian Penrose inequality is a remarkable geometric inequality between the ADM mass of an asymptotically flat manifold with non-negative scalar curvature and the area of its outermost minimal surface. A version of the Riemannian Penrose inequality has also been established for the Einstein-Maxwell equations, wh…
The positive mass theorem is one of the fundamental results in general relativity. It states that, assuming the dominant energy condition, the total mass of an asymptotically flat spacetime is non-negative. The Penrose inequality provides a lower bound on mass by the area of the black hole and is closely related to the…
This note provides an easy construction of fake octagons.
We study the Penrose transform for the `quaternionic objects' whose twistor spaces are complex manifolds endowed with locally complete families of embedded Riemann spheres with positive normal bundles.
Higher-dimensional Schwarzschild spacetimes violate the Penrose property.
In this paper, we show how to reduce the Penrose conjecture to the known Riemannian Penrose inequality case whenever certain geometrically motivated systems of equations can be solved. Whether or not these special systems of equations have general existence theories is therefore an important open problem. The key tool …
The paper proves a Penrose inequality for 4-discs with hyperbolic ends and conic singularities.