相关论文: Homological matrices
Metric currents are, in a certain sense, a metric analogous of flat currents, therefore are related to the geometry of the space and of their support. In this short note, we try to give some evidence for the previous statement, by showing…
Many first-order equational theories, such as the theory of groups or boolean algebras, can be presented by a smaller set of axioms than the original one. Recent studies showed that a homological approach to equational theories gives us…
In this note, we outline the general development of a theory of symmetric homology of algebras, an analog of cyclic homology where the cyclic groups are replaced by symmetric groups. This theory is developed using the framework of crossed…
We formulate the unitary rational orbifold conformal field theories in the algebraic quantum field theory framework. Under general conditions, we show that the orbifold of a given unitary rational conformal field theories generates a…
In this short note we provide a review of some developments in the area of homotopy quantum field theories, loosely based on a talk given by the second author at the Xth Oporto Meeting on Geometry, Topology and Physics.
Quantum computation in the one-way model requires the preparation of certain resource states known as cluster states. We describe how the construction of continuous-variable cluster states for optical quantum computing relate to the…
First we survey generating function methods for obtaining useful probability estimates about random matrices in the finite classical groups. Then we describe a probabilistic picture of conjugacy classes which is coherent and beautiful.…
We study Morse theory on noncompact manifolds equipped with exhaustions by compact pieces, defining the Morse homology of a pair which consists of the manifold and related geometric/homotopy data. We construct a collection of Morse data…
A homology and cohomology theory for topological quandles are introduced. The relation between these (co)homology groups and quandle (co)homology groups are studied. The 1 - topological quandle cocycles are used to compute state sum…
Convenient parameterizations of matrices in terms of vectors transform (certain classes of) matrix equations into covariant (hence rotation-invariant) vector equations. Certain recently introduced such parameterizations are tersely…
The paper studies the structure of restricted hom-Lie algebras. More specifically speaking, we first give the equivalent definition of restricted hom-Lie algebras. Second, we obtain some properties of $p$-mappings and restrictable hom-Lie…
We introduce the notion of the space of parallel strings with partially summable labels, which can be viewed as a geometrically constructed group completion of the space of particles with labels. We utilize this to construct a machinery…
A mathematically rigorous Hamiltonian formulation for classical and quantum field theories is given. New results include clarifications of the structure of linear fields, and a plausible formulation for nonlinear fields. Many mathematical…
We give a detailed exposition of the homotopy theory of equivalence relations, perhaps the simplest nontrivial example of a model structure.
We extend the definition of Lagrangian quantum homology to monotone Lagrangian cobordism and establish its general algebraic properties. In particular we develop a relative version of Lagrangian quantum homology associated to a cobordism…
Computing homology and cohomology is at the heart of many recent works and a key issue for topological data analysis. Among homological objects, homology generators are useful to locate or understand holes (especially for geometric…
A construction of the noncommutative-geometric counterparts of classical classifying spaces is presented, for general compact matrix quantum structure groups. A quantum analogue of the classical concept of the classifying map is introduced…
In this paper, we discuss two topics: first, we show how to convert 1+1-topological quantum field theories valued in symmetric bimonoidal categories into stable homotopical data, using a machinery by Elmendorf and Mandell. Then, we discuss,…
We present a mathematical framework for describing the topology of configuration spaces for particles on one-connected graphs. In particular, we compute the homology groups over integers for different classes of one-connected graphs. Our…
We study approximations of theories both in general context and with respect to some natural classes of theories. Some kinds of approximations are considered, connections with finitely axiomatizable theories and minimal generating sets of…