Related papers: On the Lusternik-Schnirelmann category of Peano co…

We extend the theory of the Lusternik-Schnirelmann category to general metric spaces by means of covers by arbitrary subsets. We also generalize the definition of the strict category weight. We show that if the Bockstein homomorphism on a…

Let~$G$ be a group and let~$\mathcal{F}$ be a family of subgroups of~$G$. The generalised Lusternik--Schnirelmann category~$\operatorname{cat}_\mathcal{F}(G)$ is the minimal cardinality of covers of~$BG$ by open subsets with fundamental…

Lusternik-Schnirelmann category (LS-category) of a topological space is the least integer $n$ such that there is a covering of $X$ by $n+1$ open sets, each of them being contractible in $X$. The cone length is the minimum number of…

We show that the geometry of a Riemannian manifold (M,g) is sensitive to the apparently purely homotopy-theoretic invariant of M known as the Lusternik-Schnirelmann category, denoted cat_{LS}(M). Here we introduce a Riemannian analogue of…

Let $F \hookrightarrow X \to B$ be a fibre bundle with structure group $G$, where $B$ is $(d{-}1)$-connected and of finite dimension, $d \geq 1$. We prove that the strong L-S category of $X$ is less than or equal to $m + \frac{\dim B}{d}$,…

We show that the Lusternik-Schnirelmann category of a simple, simply connected, compact Lie group G is bounded above by the sum of the relative categories of certain distinguished conjugacy classes in G corresponding to the vertices of the…

For any flag simplicial complex $K$, we describe the multigraded Poincare series, the minimal number of relations and the degrees of these relations in the Pontryagin algebra of the corresponding moment-angle complex $Z_K$. We compute the…

We reduced Rudyak's conjecture that a degree one map between closed manifolds cannot raise the Lusternik-Schnirelmann category to the computation of the category of the product of two lens spaces $L^n_p\times L_q^n$ with relatively prime…

In this paper we establish a natural definition of Lusternik-Schnirelmann category for simplicial complexes via the well known notion of contiguity. This category has the property of being homotopy invariant under strong equivalences, and…

In this paper, Lusternik-Schinrelmann and geometric category of finite spaces are considered. We define new numerical invariants of these spaces derived from the geometric category and present an algorithmic approach for its effective…

We prove a compact embedding theorem in a class of spaces of piecewise H1 functions subordinated to a class of shape regular, but not necessarily quasi-uniform triangulations of a polygonal domain. This result generalizes the…

We study the Lusternik-Schnirelmann category and topological complexity of 1-dimensional spaces. We define both invariants as lengths of suitable closed filtrations, as opposed to a more common definition based on open covers. Our main…

In this paper we estimate the Lusternik-Schnirelmann category of the connected sum of two manifolds through their categories. We achieve a more general result regarding the category of a quotient space X/A where A is a suitable subspace of…

The Lusternik-Schnirelmann category and topological complexity are important invariants of manifolds (and more generally, topological spaces). We study the behavior of these invariants under the operation of taking the connected sum of…

A criterion to determine the L-S category of a total space of a sphere-bundle over a sphere is given in terms of homotopy invariants of its characteristic map, and thus providing a complete answer to Ganea's Problem 4. As a result, we…

The simplicial LS-category of a finite abstract simplicial complex is a new invariant of the strong homotopy type, defined in purely combinatorial terms, that generalizes to arbitrary simplicial complexes the well known notion of arboricity…

We prove that the Lusternik-Schnirelmann category $cat(M)$ of a closed symplectic manifold $(M, \omega)$ equals the dimension $dim(M)$ provided that the symplectic cohomology class vanishes on the image of the Hurewicz homomorphism. This…

We determine the Lusternik-Schnirelmann category of the projective product spaces introduced by D. Davis. We also obtained an upper bound for the topological complexity of these spaces, which improves the estimate given by J. Gonz\'alez, M.…

In analogy with the classical theory of filters, for fi\-nite\-ly complete or small cat\-e\-go\-ries, we provide the concepts of fil\-ter, $\mathfrak{G}$-neigh\-bor\-hood (short for "Grothendieck-neigh\-bor\-hood") and…

Let $Q_n$ be the quasi-projective subspace of the symplectic group $\mathrm{Sp}(n)$. In this short note, we prove that the subspace Lusternik-Schnirelmann category of $Q_n$ in $\mathrm{Sp}(n)$ is 2. For that, we use a quaternionic…