Related papers: Degree formula for connective K-theory

In this paper we study the structure of $k$-transitive closures of directed paths and formulate several properties. Concept of $k$-transitive orientation generalize the traditional concept of transitive orientation of a graph.

Let $G$ be a split semisimple linear algebraic group over a field and let $X$ be a generic twisted flag variety of $G$. Extending the Hilbert basis techniques to Laurent polynomials over integers we give an explicit presentation of the…

We consider the algebraic K-theory of a truncated polynomial algebra in several commuting variables, K(k[x_1, ..., x_n]/(x_1^a_1, ..., x_n^a_n)). This naturally leads to a new generalization of the big Witt vectors. If k is a perfect field…

We show that if two rings have equivalent derived categories then they have the same algebraic K-theory. Similar results are given for G-theory, and for a large class of abelian categories.

We describe proper correspondences from graph C*-algebras to arbitrary C*-algebras by K-theoretic data. If the target C*-algebra is a graph C*-algebra as well, we may lift an isomorphism on a certain invariant to correspondences back and…

In this paper, a new invariant was built towards the classification of separable C*-algebras of real rank zero, which we call latticed total K-theory. A classification theorem is given in terms of such an invariant for a large class of…

We study the Kawai-Lewellen-Tye (KLT) relations for quantum field theory by reformulating it as an isomorphism between two Lie algebras. We also show how explicit formulas for KLT relations arise when studying rational functions on…

In this short note, we study the rank of a restricted Lie algebra $(\mathfrak{g},[p])$ and give some applications, which concerns the dimensions of non-trivial irreducible modules. We also compute the rank of the restricted contact algebra…

A k-connected graph such that deleting any edge / deleting any vertex / contracting any edge results in a graph which is not k-connected is called minimally / critically / contraction-critically k-connected. These three classes play a…

We analyze the complexity of fitting a variety, coming from a class of varieties, to a configuration of points in $\Bbb C^n$. The complexity measure, called the algebraic complexity, computes the Euclidean Distance Degree (EDdegree) of a…

In this thesis we generalise the six-term exact sequence in graded $KK$-theory obtained in a paper of Kumjian, Pask and Sims (2017) to allow correspondences with non-compact left action. In particular, this allows us to compute the graded…

We compute the generic degrees of the Ariki--Koike algebras by first constructing a basis of matrix units in the semisimple case. As a consequence, we also obtain an explicit isomorphism from any semisimple Ariki--Koike algebra to the group…

A vertex of degree one is called an end-vertex, and an end-vertex of a tree is called a leaf. A tree with at most $k$ leaves is called a $k$-ended tree. For a positive integer $k$, let $t_k$ be the order of a largest $k$-ended tree. Let…

We describe Universal Coefficient Theorems for the equivariant Kasparov theory for C*-algebras with an action of the group of integers or over a unique path space, using KK-valued invariants. We compare the resulting classification up to…

In this paper, we apply high level versions of Jacobi's derivative formula to number theory such as quarternary quadratic forms and convolution sums of some arithmetical functions.

For integer $k\geq2,$ a spanning $k$-ended-tree is a spanning tree with at most $k$ leaves. Motivated by the closure theorem of Broersma and Tuinstra [Independence trees and Hamilton cycles, J. Graph Theory 29 (1998) 227--237], we provide…

Real-world networks often exhibit strong transitivity with nontrivial local clustering spectra and degree correlations. Such features are not easily modeled in tractable network models, creating an obstacle to the theoretical understanding…

In this paper, we develop a quantitative K-theory for filtered C*-algebras. Particularly interesting examples of filtered C*-algebras include group C*-algebras, crossed product C*-algebras and Roe algebras. We prove a quantitative version…

We show that the complement of a degree $d$ hypersurface in a projective complete intersection, whose defining equations have degrees strictly larger than $d$, has a rational connectivity higher than expected. The key new feature is that a…

We provide a framework connecting several well known theories related to the linearity of graded modules over graded algebras. In the first part, we pay a particular attention to the tensor products of graded bimodules over graded algebras.…