Related papers: On the K-theoretic classification of dynamically s…
In the present work we investigate the stability of the k-essence models allowing upto quadratic terms of the kinetic energy. The system of field equations is written as an autonomous system in terms of dimensionless variables and the…
We propose efficient numerical methods for nonseparable non-canonical Hamiltonian systems which are explicit, K-symplectic in the extended phase space with long time energy conservation properties. They are based on extending the original…
We extend our previous definition of K-theoretic invariants for operator systems based on hermitian forms to higher K-theoretical invariants. We realize the need for a positive parameter $\delta$ as a measure for the spectral gap of the…
We study algebraic varieties parametrized by topological spaces and enlarge the domains of Lawson homology and morphic cohomology to this category. We prove a Lawson suspension theorem and splitting theorem. A version of Friedlander-Lawson…
We give two new conditions on topological $k$-graphs that are equivalent to the Yeend's aperiodicity Condition (A). Each of the new conditions concerns finite paths rather than infinite. We use a specific example, resulting from a new…
This paper is concerned with the algebraic K-theory of locally convex algebras stabilized by operator ideals, and its comparison with topological K-theory. We show that the obstruction for the comparison map between algebraic and…
We prove a decomposition theorem for the equivariant K-theory of actions of affine group schemes G of finite type over a field on regular separated noetherian algebraic spaces, under the hypothesis that the actions have finite geometric…
In this paper we present a new proof of the homological stability of the moduli space of closed surfaces in a simply connected background space $K$, which we denote by $S_g (K)$. The homology stability of surfaces in $K$ with an arbitrary…
We consider topological insulators and superconductors with discrete symmetries and clarify the relevant index theory behind the periodic table proposed by Kitaev. An effective Hamiltonian determines the analytical index, which can be…
This paper starts by describing the dynamics of the electron-monopole system at both classical and quantum level by a suitable reduction procedure. This suggests, in order to realise the space of states for quantum systems which are…
We investigate the topological properties of a Kitaev chain in the shape of a legged-ring, which is here referred to as Kitaev tie. We demonstrate that the Kitaev tie is a frustrated system in which topological properties are determined by…
In this paper, we compute K-theoretic $I$-function with level structure (defined by quasi-map theory) of GIT-quotient of a vector space via abelian and non-abelian correspondence. As a consequence, we generalize Givental-Lee's result to…
The tenfold way provides a strong organizing principle for invertible topological phases of matter. Mathematically, it is intimately connected with $K$-theory via the fact that there exist exactly ten Morita classes of simple real…
A new homology is defined for a non-self-adjoint operator algebra and distinguished masa which is based upon cycles and boundaries associated with complexes of partial isometries in the stable algebra. Under natural hypotheses the zeroth…
Using a result of Vdovina, we may associate to each complete connected bipartite graph $\kappa$ a $2$-dimensional square complex, which we call a tile complex, whose link at each vertex is $\kappa$. We regard the tile complex in two…
The established thermodynamic formalism of chaotic dynamics, valid at statistical equilibrium, is here generalized to systems out of equilibrium, that have yet to relax to a steady state. A relation between information, escape rate, and the…
We develop an algebraic formalism for topological $\mathbb{T}$-duality. More precisely, we show that topological $\mathbb{T}$-duality actually induces an isomorphism between noncommutative motives that in turn implements the well-known…
A new kinetic theory Boltzmann-like collision term including correlations is proposed. In equilibrium it yields the one-particle distribution function in the form of a generalised-Lorentzian resembling but not being identical with the…
The Oka principle is a heuristic in complex geometry which states that, for a wide class of complex-analytic problems concerning Stein spaces, any obstruction to finding a holomorphic solution is purely topological. A classical theorem of…
This article belongs to a subject, Directed Algebraic Topology, whose general aim is including non-reversible processes in the range of topology and algebraic topology. Here, as a further step, we also want to cover "critical processes",…