Related papers: A note about complexity of lens spaces

We prove a number of new restrictions on the enumerative properties of homology manifolds and semi-Eulerian complexes and posets. These include a determination of the affine span of the fine $h$-vector of balanced semi-Eulerian complexes…

We describe the quantization of 2-plectic manifolds as they arise in the context of the quantum geometry of M-branes and non-geometric flux compactifications of closed string theory. We review the groupoid approach to quantizing Poisson…

Twenty years ago Gromov asked about how large is the set of isomorphism classes of groups whose systolic area is bounded from above. This article introduces a new combinatorial invariant for finitely presentable groups called {\it…

Let A be an idempotent algebra on a finite domain. We combine results of Chen, Zhuk and Carvalho et al. to argue that if A satisfies the polynomially generated powers property (PGP), then QCSP(Inv(A)) is in NP. We then use the result of…

We give a characterization of critical points that allows us to define a metric invariant on all Riemannian manifolds $M$ with a lower sectional curvature bound and an upper radius bound. We show there is a uniform upper volume bound for…

We show that the decision problem for the basic system of interpretability logic IL is PSPACE-complete. For this purpose we present an algorithm which uses polynomial space with respect to the complexity of a given formula. The existence of…

We consider the strong density problem in the Sobolev space $ W^{s,p}(Q^{m};\mathscr{N}) $ of maps with values into a compact Riemannian manifold $ \mathscr{N} $. It is known, from the seminal work of Bethuel, that such maps may always be…

Cosmologists are taking a renewed interest in multiconnected spherical 3-manifolds (spherical spaceforms) as possible models for the physical universe. To understand the formation of large scale structures in such a universe, cosmologists…

Let $S$ be a minimal surface of general type with irregularity $q(S) = 1$. Well-known inequalities between characteristic numbers imply that $3 p_g(S) \le c_2(S) \le 10 p_g(S)$, where $p_g(S)$ is the geometric genus and $c_2(S)$ the…

We complement the recent theory of general singular integrals $T$ invariant under the Zygmund dilations $(x_1, x_2, x_3) \mapsto (s x_1, tx_2, st x_3)$ by proving necessary and sufficient conditions for the boundedness and compactness of…

This paper concerns harmonic analysis of the Ornstein--Uhlenbeck operator L on the Euclidean space. We examine the method of decomposing a spectral multiplier \phi(L) into three parts according to the notion of admissibility, which…

We show that if a closed oriented $n$-manifold $M$ has a non-trivial cohomology class of even degree $k$, whose all pullbacks to products of type $S^1\times N$ vanish, then the topological complexity $\mathrm{TC}(M)$ is at least $6$, if $n$…

We prove that there are 0/1 polytopes P that do not admit a compact LP formulation. More precisely we show that for every n there is a sets X \subseteq {0,1}^n such that conv(X) must have extension complexity at least 2^{n/2 * (1-o(1))}. In…

Let $X$ be a finite set in $Z^d$. We consider the problem of optimizing linear function $f(x) = c^T x$ on $X$, where $c\in Z^d$ is an input vector. We call it a problem $X$. A problem $X$ is related with linear program $\max\limits_{x \in…

We study the set of all closed oriented smooth 4-manifolds experimentally, according to a suitable complexity defined using Turaev's shadows. This complexity roughly measures how complicated the 2-skeleton of the 4-manifold is. We…

We construct new topological invariants of three-dimensional manifolds which can, in particular, distinguish homotopy equivalent lens spaces L(7,1) and L(7,2). The invariants are built on the base of a classical (not quantum) solution of…

Scharlemann and Thompson define a numerical complexity for a 3-manifold using handle decompositions of the manifold. We show that for compact hyperbolic 3-manifolds this is linearly related to a definition of metric complexity in terms of…

We study the classifying space B Diff(M) of the diffeomorphism group of a connected, compact, orientable 3-manifold M. In the case that M is reducible we build a contractible space parametrising the systems of reducing spheres. We use this…

A manifold which admits a reducible genus-$2$ Heegaard splitting is one of the $3$-sphere, $S^2 \times S^1$, lens spaces or their connected sums. For each of those splittings, the complex of Haken spheres is defined. When the manifold is…

It was shown in Alur et al. [1] that the problem of verifying finite concurrent systems through Linearizability is in EXPSPACE. However, there was still a complexity gap between the easy to obtain PSPACE lower bound and the EXPSPACE upper…