Abstract. We prove that points of a finite subset Σ ⊂ P impose independent linear conditions on homogeneous forms on P of degree ⌊nλ/2 − n⌋ in the case when at most λk points of the set Σ lie on a possibly reducible curve in P of degree k and |Σ| < λ⌈λ/2⌉, where λ is a natural number and n > 3. We apply the obtained result to threefolds having at most isolated ordinary double points. In particu...

This study aims to investigate the effects of shoe traction and obstacle height on friction during walking to better understand the mechanisms required to avoid slippage following obstacle clearance. Ten male subjects walked at a self-selected pace during eight different conditions: four obstacle heights (0%, 10%, 20% and 40% of limb length) while wearing two different pairs of shoes (low and h...

Plantar forefoot pain is common in older people and is related to increased peak pressures under the foot during gait. Variations in the hardness of the shoe sole may therefore influence both the magnitude of loading under the foot and the perceived comfort of the shoe in this population. The aim of this investigation was to determine the effect of varying shoe sole hardness on plantar pressure...

Let (V,Z) be a Topological Quantum Field Theory over a field f defined on a cobordism category whose morphisms are oriented n+1-manifolds perhaps with extra structure (for example a p1 structure and banded link). Let (M,χ) be a closed oriented n+ 1-manifold M with this extra structure together with χ ∈ H1(M). Let M∞ denote the infinite cyclic cover of M given by χ. Consider a fundamental domain...

This is a survey of some recent developments in the study of complements of line arrangements in the complex plane. We investigate the fundamental groups and finite covers of those complements, focusing on homological and enumerative aspects. The unifying framework for this study is the stratification of the character variety of the fundamental group, G, by the jumping loci for cohomology with ...

The following divisors in the space Sym12 P1 of twelve points on P 1 are actually the same: (A) The possible locus of the twelve nodal fibers in a rational elliptic fibration (i.e. a pencil of plane cubic curves); (B) degree 12 binary forms that can be expressed as a cube plus a square; (C) the locus of the twelve tangents to a smooth plane quartic from a general point of the plane; (D) the bra...

Recently, Mullins calculated the Casson-Walker invariant of the 2-fold cyclic branched cover of an oriented link in S in terms of its Jones polynomial and its signature, under the assumption that the 2-fold branched cover is a rational homology 3-sphere. Using elementary principles, we provide a similar calculation for the general case. In addition, we calculate the LMO invariant of the p-fold ...

Let W → A be the universal Weierstrass family of cubic curves over C. For each N ≥ 2, we construct surfaces parameterizing the three standard kinds of level N structures on the smooth fibers of W . We then complete these surfaces to finite covers of A. Since W → A is the versal deformation space of a cusp singularity, these surfaces convey information about the level structure on any family of ...

This is a survey of some recent developments in the study of complements of line arrangements in the complex plane. We investigate the fundamental groups and nite covers of those complements, focusing on homological and enumerative aspects. The unifying framework for this study is the strati-cation of the character variety of the fundamental group, G, by the jumping loci for cohomology with coe...

Ozsváth and Szabó defined an analog of the Frøyshov invariant in the form of a correction term for the grading in Heegaard Floer homology. Applying this to the double cover of the 3-sphere branched over a knot K, we obtain an invariant δ of knot concordance. We show that δ is determined by the signature for alternating knots and knots with up to nine crossings, and conjecture a similar relation...