Related papers: A geometric proof of the classification of complex…

We prove a connectedness result for products of weighted projective spaces.

We examine the topological characteristic cohomology classes of complexified vector bundles. In particular, all the classes coming from the real vector bundles underlying the complexification are determined.

We study the complexity of locally checkable labeling (LCL) problems on $\mathbb{Z}^n$ from the point of view of descriptive set theory, computability theory, and factors of i.i.d. Our results separate various complexity classes that were…

We show that determining the crossing number of a link is NP-hard. For some weaker notions of link equivalence, we also show NP-completeness.

We introduce a common generalization of the L-R-smash product and twisted tensor product of algebras, under the name L-R-twisted tensor product of algebras. We investigate some properties of this new construction, for instance we prove a…

If $E$ is a directed graph and $K$ is a field, the Leavitt path algebra $L_K(E)$ of $E$ over $K$ is naturally graded by the group of integers $\mathbb Z.$ We formulate properties of the graph $E$ which are equivalent with $L_K(E)$ being a…

We give some properties of cosymplectic Lie algebras, we show, in particular, that they support a left symmetric product. We also give some constructions of cosymplectic Lie algebras, as well as a classification in three and…

In this note we give a short and elementary proof for a part of Amitsur's noncrossed product theorem. Our approach does not rely on well-known results of valuation theory. Instead, we employ some preliminary properties of the unit groups of…

We give a short proof for a well-known formula for the rank of a $G$-crossed braided extension of a modular tensor category.

We define the geometric complex associated to a Morse-Bott-Smale vector field, cf. [Austin-Braam, 1995], and its associated spectral sequence. We prove an extension of the Bismut-Zhang theorem to Morse-Bott-Smale functions. The proof is…

We construct the crossed product of a C(X)-algebra by an endomorphism, in such a way that it becomes induced by a Hilbert C(X)-bimodule. Furthermore we introduce the notion of C(X)-category, and discuss relationships with crossed products…

We prove the strong form of the Gaussian product conjecture in dimension three. Our purely analytical proof simplifies previously known proofs based on combinatorial methods or computer-assisted methods, and allows us to solve the case of…

We introduce a notion of c-group, which is a group up to congruence relation and consider the corresponding category. Extensions, actions and crossed modules (c-crossed modules) are defined in this category and the semi-direct product is…

We give completely combinatorial proofs of the main results of [3] using polygons. Namely, we prove that the mapping class group of a surface with boundary acts faithfully on a finitely-generated linear category. Along the way we prove some…

We give a direct combinatorial proof that the product of two descent classes in a symmetric group is a sum of descent classes. The proof is based on the fact that the group product gives a covering map when descent classes are endowed with…

We generalize the tensor product theory for modules for a vertex operator algebra previously developed in a series of papers by the first two authors to suitable module categories for a ''conformal vertex algebra'' or even more generally,…

We construct homology theories with coefficients in L-spectra on the category of ball complexes and we define products in this setting. We also obtain signatures of geometric situations in these homology groups and prove product formulae…

The paper presents a construction of the crossed product of a C*-algebra by a semigroup of endomorphisms generated by partial isometries.

Complex vector analysis is widely used to analyze continuous systems in many disciplines, including physics and engineering. In this paper, we present a higher-order-logic formalization of the complex vector space to facilitate conducting…

Using a homological invariant together with an obstruction class in a certain Ext^2-group, we may classify objects in triangulated categories that have projective resolutions of length two. This invariant gives strong classification results…