Related papers: Relations among higher Whitehead maps
We study the construction of tensor products of representations up to homotopy, which are the A-infinity version of ordinary representations. We provide formulas for the construction of tensor products of representations up to homotopy and…
We show that both Lusternik-Schnirelmann category and topological complexity are particular cases of a more general notion, that we call homotopic distance between two maps. As a consequence, several properties of those invariants can be…
Multipath cohomology is a cohomology theory for directed graphs, which is defined using the path poset. The aim of this paper is to investigate combinatorial properties of path posets, and to provide computational tools for multipath…
We give a general formula relating self cup products in cohomology to connecting maps in nonabelian cohomology, and apply it to obtain a formula for the self cup product associated to the Weil pairing.
The object of this paper is the tameness conjecture which describes an arbitrary graded k-algebra homomorphism of polytopal rings. We give further evidence of this conjecture by showing supporting results concerning joins, multiples and…
We bring a linkage from representation theory of Lie groups to homotopy theory for maps between flag manifolds. As applications we derive from representation theory abundant families of homotopy classes of maps between flag manifolds whose…
In this note, we extend the definition of $p$-biharmonic and bi-$p$-harmonic maps between two Riemannian manifolds and explore some of their properties.
Higher order networks are able to characterize data as different as functional brain networks, protein interaction networks and social networks beyond the framework of pairwise interactions. Most notably higher order networks include…
We show that $v_n$-periodic homotopy groups detect homotopy equivalences between simply-connected finite CW-complexes.
Golodness of 2-dimensional simplicial complexes is studied through polyhedral products, and combinatorial and topoogical characterization of Golodness of surface triangulations is given. An answer to the question of Berglund is also given…
This paper is a fundamental study of comodules and contramodules over a comonoid in a symmetric closed monoidal category. We study both algebraic and homotopical aspects of them. Algebraically, we enrich the comodule and contramodule…
We investigate relative holomorphic connections on a principal bundle over a family of compact complex manifolds. A sufficient condition is given for the existence of a relative holomorphic connection on a holomorphic principal bundle over…
Differentiable conjugacies link dynamical systems that share properties such as the stability multipliers of corresponding orbits. It provides a stronger classification than topological conjugacy, which only requires qualitative similarity.…
This article studies a large, general class of orthogonal polytopes which we may call "generic orthotopes". These objects emerged from a desire to represent a Coxeter complex by an orthogonal polytope that is particularly nice with respect…
We introduce higher simplicial complexity of a simplicial complex $K$ and higher combinatorial complexity of a finite space $P$ (i.e. $P$ is a finite poset). We relate higher simplicial complexity with higher topological complexity of $|K|$…
We introduce a notion of discrete topological complexity in the setting of simplicial complexes, using only the combinatorial structure of the complex by means of the concept of contiguous simplicial maps. We study the links of this new…
As part of various obstruction theories, non-trivial Massey products have been studied in symplectic and complex geometry, commutative algebra and topology for a long time. We introduce a general approach to constructing non-trivial Massey…
The Sierpi\'nski product of graphs generalises the vast and relevant class of Sierpi\'nski-type graphs, and is also related to the classic lexicographic product of graphs. Our first main results are necessary and sufficient conditions for…
Two homotopy decompositions of supensions of spaces involving polyhedral products are given. The first decomposition is motivated by the decomposition of suspensions of polyhedral products by Bahri, Bendersky, Cohen, and Gitler, and is a…
In [8] a notion of generalized Hadamard product was introduced. We show that when certain kinds of tensors interact with the eigenvalues of symmetric matrices the resulting formulae can be nicely expressed using the generalized Hadamard…