arXiv research

The aim of this paper is to develop on the 1-jet space J^1(R,M^4) the Finsler-like geometry (in the sense of d-connection, d-torsions and d-curvatures) of the rheonomic Berwald-Moor metric. A natural geometrical gravitational field theory produced by the rheonomic Berwald-Moor metric is also constructed.

Describes the relationship between two spectral sequences and their joint refinement.

In this paper we construct the differential equations of the stream lines that characterize plasma regarded as a non-isotropic medium geometrized by a jet rheonomic time-invariant Berwald-Moor metric. Section 1 contains historical notes regarding the Plasma Physics and its geometrical description. Section 2 analyzes th…

The paper proves properties of manifolds under certain conditions.

Space exploration technology advances exponentially, consistent with Moore's and Wright's laws.

Geometrically studies Moore-Penrose inverse and polar decomposition continuity.

In this paper we expose on the dual 1-jet space J^{1*}(R,M^4) the distinguished (d-) Riemannian geometry (in the sense of d-connection, d-torsions, d-curvatures and some gravitational-like and electromagnetic-like geometrical models) for the (t,x)-conformal deformed Berwald-Moor Hamiltonian metric of order four.

We introduce a construction adding low-dimensional cells to a space that satisfies certain low-dimensional conditions; it preserves high-dimensional homology with appropriate coefficients. This includes as special cases Quillen's plus construction, Bousfield's integral homology localization, the existence of Moore spac…

The aim of this paper is to develop on the 1-jet space J^1(R, M^n) the Finsler-like geometry (in the sense of distinguished (d-) connection, d-torsions, d-curvatures and some gravitational-like and electromagnetic-like geometrical models) attached to the (t,x)-conformal deformation of the Berwald-Moor metric.

The paper determines modular cohomotopy groups up to extensions using classical and unstable homotopy methods.

The aim of this paper is to develop on the 1-jet space J^1(R,M^3) the Finsler-like geometry (in the sense of distinguished (d-) connection, d-torsions and d-curvatures) of the rheonomic Berwald-Moor metric of order three. Some natural geometrical field theories (gravitational and electromagnetic) produced by the preced…

We give an updated extended survey of results related to the celebrated unsolved generalized R. L. Moore problem. In particular, we address the problem of characterizing codimension one manifold factors, i.e. spaces $X$ having the property that $X \times \mathbb{R}$ is a topological manifold. A main part of the paper i…

We describe an explicit semi-algebraic partition for the complement of a real hyperplane arrangement such that each piece is contractible and so that the pieces form a basis of Borel-Moore homology. We also give an explicit correspondence between the de Rham cohomology and the Borel-Moore homology.

We show that a Moore space M(Z_m,1) is an absolute extensor for finite dimensional metrizable spaces of cohomological dimension dim_{Z_m} \leq 1.

The aim of this paper is to expose some geometrical properties of the locally Minkowski-Cartan space with the Berwald-Moor metric of momenta. This space is regarded as a particular case of the $m$-th root Cartan space. Thus, Section 2 studies the $v$-covariant derivation components of the $m$-th root Cartan space. Sect…

Survey and generalization of implosion and contraction in symplectic and hyperkähler geometry.

In this paper we parametrize the symmetry group of the n-dimensional Berwald-Moor metric. Some properties of this Lie group are studied, and its corresponding Lie algebra is computed.

The study proves conditions for constant curvature submanifolds in space forms.

The BPS decomposition theorem splits cohomology of symmetric stacks into invariant parts.

Constructs hyper-Kähler models using Riemann-Hilbert problems.

Complete description of BNSR invariants for Lodha-Moore groups, proving finiteness properties.

We study hyperkahler metrics and hyperholomorphic connections of Hitchin's moduli spaces after Gaiotto, Moore and Neitzke. Their construction via the twistor technique produces intricate wall crossing behaviors. For certain four dimensional Hitchin's moduli spaces local models and degeneration to local models near sing…

Novel construction of Bauer--Furuta invariant using sheaves of spectra.

New groups can't be fundamental groups of symplectic Calabi-Yau manifolds.

For each integer $N\geq 2$, Mariño and Moore defined generalized Donaldson invariants by the methods of quantum field theory, and made predictions about the values of these invariants. Subsequently, Kronheimer gave a rigorous definition of generalized Donaldson invariants using the moduli spaces of anti-self-dual conne…

We consider Hitchin's hyperkähler metric $g_{L^2}$ on the $SU(n)$-Hitchin moduli space moduli space over a compact Riemann surface. We prove that the difference between the metric $g_{L^2}$ and a simpler "semiflat" hyperkähler metric $g_{\mathrm{sf}}$ is exponentially-decaying along generic rays in the Hitchin moduli s…

Certain six-dimensional (1,0) supersymmetric little string theories, when compactified on $T^3$, have moduli spaces of vacua given by smooth K3 surfaces. Using ideas of Gaiotto-Moore-Neitzke, we show that this provides a systematic procedure for determining the Ricci-flat metric on a smooth K3 surface in terms of BPS d…

Generalized Donaldson invariants of 4-manifolds are defined, using moduli spaces of anti-self-dual connections with structure group SU(N) or PSU(N). Some values of the invariants are calculated for the case that the 4-manifold arises by the knot-complement construction of Fintushel and Stern. The results are consistent…

In this article we show that some of the recent results of Marino, Moore, and Peradze (math.DG/9812042, hep-th/9812055) -- in particular their conjecture that all closed, smooth four-manifolds with b_2^+ > 1 (and Seiberg-Witten simple type) are of `superconformal simple type' -- can be understood using a simple mathema…

Using Hirasawa-Murasugi's classification of fibered Montesinos knots we classify the L-space Montesinos knots, providing further evidence towards a conjecture of Lidman-Moore that L-space knots have no essential Conway spheres. In the process, we classify the fibered Montesinos knots whose open books support the tight …

Defines formal vertex laws related to Lie conformal algebras.

Let Map(K,X) denote the space of pointed continuous maps from a finite cell complex K to a space X. Let E_* be a generalized homology theory. We use Goodwillie calculus methods to prove that under suitable conditions on K and X, Map(K, X) will send a E_*--isomorphism in either variable to a map that is monic in E_* hom…

We define general rotational surfaces of elliptic and hyperbolic type in the pseudo-Euclidean 4-space with neutral metric which are analogous to the general rotational surfaces of C. Moore in the Euclidean 4-space. We study Lorentz general rotational surfaces with plane meridian curves and give the complete classificat…

Study configuration spaces of punctured spaces, focusing on homology and group actions.

We prove that any compact four-manifold admits a Riemannian metric with negative isotropic curvature in the sense of Micallef and Moore.

General rotational surfaces as a source of examples of surfaces in the four-dimensional Euclidean space have been introduced by C. Moore. In this paper we consider the analogue of these surfaces in the Minkowski 4-space. On the base of our invariant theory of spacelike surfaces we study general rotational surfaces with…

Let $G/K$ be an irreducible Hermitian symmetric spaces of compact type with the standard homogeneous complex structure. Then the real symplectic manifold $(T^*(G/K),Ω)$ has the natural complex structure $J^-$. We construct all $G$-invariant Kähler structures $(J,Ω)$ on homogeneous domains in $T^*(G/K)$ anticommuting wi…

We describe the orbit space of the action of the group $\mathrm{Sp}(2)\mathrm{Sp}(1)$ on the real Grassmann manifolds $\mathrm{Gr}_k(\mathbb{H}^2)$ in terms of certain quaternionic matrices of Moore rank not larger than $2$. We then give a complete classification of valuations on the quaternionic plane $\mathbb{H}^2$ w…

Proves special alternating knots can't have cosmetic crossings.

The paper constructs homotopically non-trivial spheres in complexified spaces.

In their previous work, Barraud and Cornea enriched the Lagrangian Floer complex by adding cubical chains in the based loop space of the Lagrangian, and recovered the Leray-Serre spectral sequence of the based path space fibration, assuming that the Lagrangian is weakly exact and simply connected. In the present articl…

Study constructs solutions for evolving hypersurfaces using inverse spacetime mean curvature.

In this note we revisit the subject of anomaly cancelation in string theory and M-theory on manifolds with String structure and give three observations. First, that on String manifolds there is no E8 x E8 global anomaly in heterotic string theory. Second, that the description of the anomaly in the phase of the M-theory…

New algorithm finds more arbitrage opportunities in DEXs.

Given two compact n-dimensional manifolds in the smooth, piecewise linear or topological categories, basic results of B. Mazur and others give simple criteria for determining whether their products with Euclidean spaces of sufficiently large dimension are isomorphic in the given category. This paper studies such questi…

New curvature measure for graphs improves diameter and eigenvalue estimates.

We review a construction of hyperkahler metrics proposed in joint work of Davide Gaiotto, Greg Moore and the author. A key ingredient in this construction is a collection of integer "DT invariants" obeying the wall-crossing formula of Kontsevich-Soibelman.

Classical and quantum Chern-Simons with gauge group $\text{U}(1)^N$ were classified by Belov and Moore in \cite{belov_moore}. They studied both ordinary topological quantum field theories as well as spin theories. On the other hand a correspondence is well known between ordinary $(2+1)$-dimensional TQFTs and modular te…