相关论文: Higher simple structure sets of lens spaces with t…

We give simple upper bounds for rational sectional category and use them to compute invariants of the type of Farber's topological complexity of rational spaces. In particular we show that the sectional category of formal morphisms reaches…

Given a simplicial complex $X$, we construct a simplicial complex $\Omega X$ that may be regarded as a combinatorial version of the based loop space of a topological space. Our construction explicitly describes the simplices of $\Omega X$…

Let $p$ be a prime. In this paper, we compute complexities of some simple modules of symmetric groups labelled by two-part partitions. Most of the simple modules considered here are contained in the $p$-blocks with non-abelian defect…

We construct a solvable group G of order 5648590729620 such that the set of element orders of G coincides with that of the simple group S(4,3). This completes the determination of finite simple groups isospectral to solvable groups.

We describe the generic modules in each component of the spaces of representations of certain string algebras. In so doing, we calculate the dimensions of higher self-extension groups for generic modules. This algorithm lends itself for use…

In this, largely expository, note, we show how the simplicial structure of the moduli spaces of stable rational curves with marked points allows to produce explicit equations for these spaces. The key argument is an elementary combinatorial…

We construct smooth bundles with base and fiber products of two spheres whose total spaces have non-vanishing $\hat{A}$-genus. We then use these bundles to locate non-trivial rational homotopy groups of spaces of Riemannian metrics with…

Third-order ordinary differential equations with Lie symmetry algebras isomorphic to the nonsolvable algebra $\mathfrak{sl}(2,\mathbb{R})$ admit solvable structures. These solvable structures can be constructed by using the basis elements…

The global geometry of the moduli spaces of higher spin curves and their birational classification is largely unknown for g >= 2 and r > 2. Using quite related geometric constructions, we almost complete the picture of the known results in…

We compute the reduced cosmic shear up to second order in the gravitational potential without relying on the small angle or thin-lens approximation. This is obtained by solving the Sachs equation which describes the deformation of the…

Multiple image gravitational lens systems, and especially quads are invaluable in determining the amount and distribution of mass in galaxies. This is usually done by mass modeling using parametric or free-form methods. An alternative way…

This is a survey of our research on geometric structures of projective embeddings and includes some topics of our talks in several symposia during 1990-99. We clarify our main problem, which is to construct a kind of geometric composition…

In this paper, we identify the concordance classes of smooth structures on $PL$-manifolds of dimension between $8$ and $10$ in terms of the cohomology and Steenrod operations. This leads to the computation of the homotopy inertia groups.…

We classify the simple even lattices of square free level and signature (2,n) for n > 3. A lattice is called simple if the space of cusp forms of weight 1+n/2 for the dual Weil representation of the lattice is trivial. For a simple lattice…

We consider simplicial sets equipped with a notion of smallness, and observe that this slight "topological" extension of the "algebraic" simplicial language allows a concise reformulation of a number of classical notions in topology, e.g.…

We give very flexible, concrete constructions of discrete and faithful epresentations of right-angled Artin groups into higher-rank Lie groups. Using the geometry of the associated symmetric spaces and the combinatorics of the groups, we…

As an important candidate theory of gravity, Brans-Dicke theory has been widely studied. In this paper, we investigate light bending and gravitational lensing by compact objects in Brans-Dicke theory in weak gravitational field. Firstly, we…

In this paper we develop a method for studying tight contact structures on lens spaces. We then derive uniqueness and non-existence statements for tight contact structures with certain (half) Euler classes on lens spaces. We also prove that…

We study the structures of arbitrary split Leibniz triple systems. By developing techniques of connections of roots for this kind of triple systems, under certain conditions, in the case of $T$ being of maximal length, the simplicity of the…

This paper describes the homology of various simplicial complexes associated to set families from combinatorial number theory, including primitive sets, pairwise coprime sets, product-free sets, and coprime-free sets. We present a condition…