Related papers: $J^+$-like Invariants under Bifurcations

Let $A\to C$ be a proper surjective morphism from a smooth connected quasi-projective commutative group scheme of dimension 2 to a smooth curve. The construction of generalized Kummer varieties gives a proper morphism $A^{[[n]]}\to…

Let $N$ (resp., $U$) be a manifold (resp., an open subset of $\mathbb{R}^m$). Let $f:N\to U$ and $F:U\to \mathbb{R}^\ell$ be an immersion and a $C^{\infty}$ mapping, respectively. Generally, the composition $F\circ f$ does not necessarily…

We consider the possibility of a control field opening up multiple pathways and thereby leading to new interference and coherence effects. We illustrate the idea by considering the $J=1/2\leftrightarrow J=1/2$ transition. As a result of the…

We study a class of bifurcations generically occurring in dynamical systems with non-mutual couplings ranging from models of coupled neurons to predator-prey systems and non-linear oscillators. In these bifurcations, extended attractors…

We identify two rather novel types of (compound) dynamical bifurcations generated primarily by interactions of an invariant attracting submanifold with stable and unstable manifolds of hyperbolic fixed points. These bifurcation types -…

A class of shape-invariant bound-state problems which represent two-level systems are introduced. It is shown that the coupled-channel Hamiltonians obtained correspond to the generalization of the Jaynes-Cummings Hamiltonian.

In this paper we define two regular homotopy invariants c and i for immersions of oriented 3-manifolds into R^5 in a geometric manner. The pair (c(f),i(f)) completely describes the regular homotopy class of the immersion f. The invariant i…

The wall-crossing formula for Donaldson invariants of smooth, simply connected four manifolds with $b^+=1$ is shown to be a topological invariant of the manifold for reducible connections with two or fewer singular points. The explicit…

We give a classification of generic coadjoint orbits for the group of area-preserving diffeomorphisms of a closed non-orientable surface. This completes V. Arnold's program of studying invariants of incompressible fluids in 2D. As an…

Hamiltonian bifurcations in the context of noncanonical Hamiltonian matter models are described. First, a large class of 1 + 1 Hamiltonian multi-fluid models is considered. These models have linear dynamics with discrete spectra, when…

We study generalized diffeomorphisms in exceptional geometry with U-duality group E_{n(n)} from an algebraic point of view. By extending the Lie algebra e_n to an infinite-dimensional Borcherds superalgebra, involving also the extension to…

The class of special generic maps contains Morse functions with exactly two singular points, characterizing spheres topologically which are not $4$-dimensional and the $4$-dimensional unit sphere. This class is for higher dimensional…

Given two smooth, oriented, closed 4-manifolds $M_1$ and $M_2$, we construct two invariants, $D^P(M_1, M_2)$ and $D(M_1, M_2)$, coming from distances in the pants complex and the dual curve complex respectively. To do this, we adapt work of…

We introduce the notion of mc-biquandles, algebraic structures which have possibly distinct biquandle operations at single-component and multi-component crossings. These structures provide computable homset invariants for classical and…

This work addresses the existence of transitive extensions of certain infinite permutation groups which arise as the automorphism groups of model-theoretic structures which are generic in the Fra\"iss\'e sense. The study of transitive…

We study the Donaldson invariants of simply connected $4$-manifolds with $b_+=1$, and in particular the change of the invariants under wall-crossing. We assume the conjecture of Kotschick and Morgan about the shape of the wall-crossing…

We introduce a method that generates invariant functions from perturbative classical field theories depending on external parameters. Applying our methods to several field theories such as abelian BF, Chern-Simons and 2-dimensional…

In this paper we discuss the applications of knotoids to modelling knots in open curves and produce new knotoid invariants. We show how invariants of knotoids generally give rise to well-behaved measures of how much an open curve is…

We prove that immersions of planar domains are uniquely specified by their Jacobian determinant, curl function, and boundary values. This settles the two-dimensional version of an outstanding conjecture related to a particular grid…

A class of shape-invariant bound-state problems which represent transitions in a two-level system introduced earlier are generalized to include arbitrary energy splittings between the two levels. We show that the coupled-channel…