Related papers: The 4-Dimensional Light Bulb Theorem (after David …
The above named paper has been withdrawn. A colleague has observed a gap in the proof of isotopy invariance, which can be repaired by reducing the coefficients (which lie in (1/6)Z) of the antisymmetric kanji with chords incident with more…
The Standard Model of elementary particle physics is one of the most successful models of contemporary theoretical physics being in full agreement with experiments. However, its mathematical structure deserves further investigations both…
The basis of new ideas in the old theory is the Majorana and Ahluwalia constructs, modified versions of the Weinberg $2(2j+1)$ theory, and the Barut's self-field quantum electrodynamics.
In this letter we show that the soft behaviour of photons and graviton amplitudes, after projection, can be determined to infinite order in soft expansion via ordinary on-shell gauge invariance. In particular, as one of the particle's…
A classical problem in algebraic geometry is to construct smooth algebraic varieties with prescribed properties. In the approach via smoothings, one first constructs a degenerate scheme with the prescribed properties, and then shows the…
Recall that the moduli space of smooth (that is, stable) cubic curves is isomorphic to the quotient of the upper half plane by the group of fractional linear transformations with integer coefficients. We establish a similar result for…
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The well-known 5-parameter isometry group of plane gravitational waves in $4$ dimensions is identified as Levy-Leblond's Carroll group in $2+1$ dimensions with no rotations. Our clue is that plane waves are Bargmann spaces into which…
The concept of only One-dimensional time is wrong, time is Four-dimensional. The light refraction emerges directly that time is four-dimensional to us perfectly. It translates some thing incomprehensible into easily comprehensible in…
It is shown that all predictions for the light scalars, based on their four-quark nature, are supported by experiment. The future research program is outlined also.
This thesis develops a general theoretical and numerical framework for achieving high-contrast atom interferometry based on double Bragg diffraction (DBD). While DBD offers intrinsic symmetry, reduced sensitivity to internal-state…
We discuss some aspects of F-theory in four dimensions on elliptically fibered Calabi-Yau fourfolds which are Calabi-Yau threefold fibrations. A particularly simple class of such manifolds emerges for fourfolds in which the generic…
We modify the proof of the disc embedding theorem for $4$-manifolds, which appeared as Theorem 5.1A in the book "Topology of 4-manifolds" by Freedman and Quinn, in order to construct geometrically dual spheres. These were claimed in the…
In this work methods of construction of cubic graphs are analyzed and a theorem of existence of a colored disc traversing each pair of linked edges belonging to an elementary cycle of a planar cubic graph is proved.
In this paper we present the Braid Monodromy Type (BMT) of curves and surfaces; past, present and future. The BMT is an invariant that can distinguish between non-isotopic curves; between different families of surfaces of general type;…
We show that the smooth geometry of a hyperbolic 3-manifold emerges from a classical spin system defined on a 2d discrete lattice, and moreover show that the process of this "dimensional oxidation" is equivalent with the dimensional…
The generalized definition of symmetry is formulated. Application of this definition for symmetric analysis of theoretical physics equations is considered. The version of electrodynamics is constructed permitting the faster-than-light…
We present a pair of open smooth $4$-manifolds that are mutually homeomorphic. One of them admits a Riemannian metric that possesses quasi-cylindricity, and positivity of scalar curvature and of dimension of certain $L^2$ harmonic forms. By…
The polynomial invariants $q_d$ for a large class of smooth 4-manifolds are shown to satisfy universal relations. The relations reflect the possible genera of embedded surfaces in the 4-manifold and lead to a structure theorem for the…
This paper explains the recent developments on the symplectic theory of Hamiltonian completely integrable systems on symplectic 4-manifolds, compact or not. One fundamental ingredient of these developments has been the understanding of…