On relations between 1-lines of Adams–Novikov spectral sequences modulo invariant prime ideals

We have a ring homomorphism Θ from the cohomology of the extended Morava stabilizer group G_n with coefficients in F[w^±1] to the cohomology of G_n+1 with coefficients in the graded field F((u_n))[u^±1]. In this note we study the behavior of Θ on H¹. Then it is shown that Θ is injective on H¹ for n1 and for all primes p.     

A non-normal topology generated by a two-point selection

We construct a two-point selection , where is the set of the irrational numbers, such that the space is not normal and it is not collectionwise Hausdorff either. Here, τ_f denotes the topology generated by the two-point selection f. This example answers a question posed by V. Gutev and T. Nogura. We also show that if is a two-point selection such that the topology τ_f has countable pseudocharacter, then τ_f is a Tychonoff topology.     

Peripheral polynomials of hyperbolic knots

If K is a hyperbolic knot in S³, an algebraic component of its character variety containing one holonomy of the complete hyperbolic structure of finite volume of S³K is an algebraic curve . The traces of the peripheral elements of K define polynomial functions in , which are related in pairs by polynomials (peripheral polynomials). These are determined by just two adjacent peripheral polynomials. The curves defined by the peripheral polynomials are all birationally equivalent to , with only one possible exception. The canonical peripheral polynomial relating the trace of the meridian with the trace of the canonical longitude of K, is a factor of the A-polynomial.     

Isovariant maps from free -manifolds to representation spheres

The isovariant version of Borsuk–Ulam type theorems has been studied by Wasserman and the first author. In this paper, first we consider the relation between the existence of C_n-isovariant maps from free C_n-manifolds to representation spheres and Borsuk–Ulam type inequalities for their dimensions. Our main result classifies the C_n-isovariant maps by C_n-isovariant homotopy types when a Borsuk–Ulam type inequality holds. For proving it, we use the multidegree of a C_n-equivariant map developed by the first author.     

Nonlinear maps preserving Lie products on factor von Neumann algebras

In this paper, we prove that every bijective map preserving Lie products from a factor von Neumann algebra into another factor von Neumann algebra is of the form A→ψ(A)+ξ(A), where is an additive isomorphism or the negative of an additive anti-isomorphism and is a map with ξ(AB-BA)=0 for all .     

On -differential graded algebras

We introduce the concept of N-differential graded algebras (N-dga), and study the moduli space of deformations of the differential of an N-dga. We prove that it is controlled by what we call the (M,N)-Maurer–Cartan equation.     

Uniform asymptotic expansions of the Pollaczek polynomials

Two uniform asymptotic expansions are obtained for the Pollaczek polynomials P_n(cosθ;a,b). One is for , , in terms of elementary functions and in descending powers of . The other is for , in terms of a special function closely related to the modified parabolic cylinder functions, in descending powers of n. This interval contains a turning point and all possible zeros of P_n(cosθ) in θ(0,π/2].     

Coclass and cohomology

Recently, it was proved by Leedham-Green and others that with a finite number of exceptions, every p-group of coclass r is a quotient of one of only a finite number of p-adic uniserial space groups. In this paper we use that structure to demonstrate that there are only finitely many isomorphism classes of cohomology rings of 2-groups of coclass r with coefficients in any fixed field k of characteristic 2. In addition, there is experimental evidence indicating that in many cases successive quotients of the uniserial space groups have isomorphic cohomology rings.     

Buchsbaum homogeneous algebras with minimal multiplicity

In this paper we first give a lower bound on multiplicities for Buchsbaum homogeneous k-algebras A in terms of the dimension d, the codimension c, the initial degree q, and the length of the local cohomology modules of A. Next, we introduce the notion of Buchsbaum k-algebras with minimal multiplicity of degree q, and give several characterizations for those rings. In particular, we will show that those algebras have linear free resolutions. Further, we will give many examples of those algebras.     

On periodic radical groups in which permutability is a transitive relation

A group G is said to be a -group if permutability is a transitive relation in the set of all subgroups of G. Our purpose in this paper is to study -groups in the class of periodic radical groups satisfying min-p for all primes p.     

Limit shape of convex lattice polygons with minimal perimeter

Let n be a positive integer and · any norm in . Denote by B the unit ball of · and the class of convex lattice polygons with n vertices and least ·-perimeter. We prove that after suitable normalization, all members of tend to a fixed convex body, as n→∞.     

Differentiability of torsion theories

We prove that every perfect torsion theory for a ring R is differential (in the sense of [P.E. Bland, Differential torsion theory, Journal of Pure and Applied Algebra 204 (2006) 1–8]). In this case, we construct the extension of a derivation of a right R-module M to a derivation of the module of quotients of M. Then, we prove that the Lambek and Goldie torsion theories for any R are differential.     

Unitarizability of premodular categories

We study the unitarizability of premodular categories constructed from representations of quantum group at roots of unity. We introduce Grothendieck unitarizability as a natural generalization of unitarizability to classes of premodular categories with a common Grothendieck semiring. We obtain new results for quantum groups of Lie types F₄ and G₂, and improve the previously obtained results for Lie types B and C.     

Fractal sets determined by dilation-stable processes

Let be a dilation-stable process on . We determine a Hausdorff measure function (a) such that the fractal set X[0,1]={X(t):0t1} has positive finite -measure. We also investigate the packing measure of X[0,1].     

Maximal realcompact spaces and measurable cardinals

Comfort and Hager investigate the notion of a maximal realcompact space and ask about the relationship to the first measurable cardinal . A space is said to be a space if the intersection of fewer than open sets is again open. They ask if each realcompact space is maximal realcompact. We establish that this question is undecidable.     

A survey on proper codes

The performance of a linear t-error correcting code over a q-ary symmetric memoryless channel with symbol error probability ε is characterized by the probability that a transmission error will remain undetected. This probability is a function of ε involving the code weight distribution and the weight distribution of the cosets of minimum weight at most t. When the undetectable error probability is an increasing function of ε, the code is called t-proper.

The paper presents sufficient conditions for t-properness and a list of codes known to be proper, many of which have been studied by these sufficient conditions. Special attention is paid to error detecting codes of interest in modern communication.     

Imaginary automorphisms on real hyperelliptic curves

A real hyperelliptic curve X is said to be Gaussian if there is an automorphism such that , where [-1] denotes the hyperelliptic involution on X. Gaussian curves arise naturally in several contexts, for example when one studies real Jacobians. In the present paper, we study the properties of Gaussian curves and we describe their moduli spaces.     

Pseudoarcs, pseudocircles, Lakes of Wada and generic maps on

We prove a Bruckner–Garg type theorem for the fiber structure of a generic map from a continuum X into the unit interval I. We also study the specific case of X=S². We show that each nondegenerate component of each fiber of a generic map in C(S²,I) is figure-eight-like. This together with a result by Krasinkiewicz and Levin gives that each nondegenerate component of each fiber of a generic map in C(S²,I) is hereditarily indecomposable and figure-eight-like. We also show that pseudoarcs, pseudocircles and Lakes of Wada appear in abundance in fibers of a generic map in C(S²,I). We also exhibit a general method for proving when a P-like hereditarily indecomposable continuum is Q-like when Q is a certain graph containing P.     

Jumps in cohomology and free group actions

A discrete group G has periodic cohomology over R if there is an element in a cohomology group cup product with which it induces an isomorphism in cohomology after a certain dimension. Adem and Smith showed that if , then this condition is equivalent to the existence of a finite dimensional free-G-CW-complex homotopy equivalent to a sphere. It has been conjectured by Olympia Talelli, that if G is also torsion-free then it must have finite cohomological dimension. In this paper we use the implied condition of jump cohomology over R to prove the conjecture for -groups and solvable groups. We also find necessary conditions for free and proper group actions on finite dimensional complexes homotopy equivalent to closed, orientable manifolds.     

General preservers of invariant subspace lattices

Let be the space of all bounded linear operators on a Banach space X and let LatA be the lattice of invariant subspaces of the operator . We characterize some maps with one of the following preserving properties: Lat(Φ(A)+Φ(B))=Lat(A+B), or Lat(Φ(A)Φ(B))=Lat(AB), or Lat(Φ(A)Φ(B)+Φ(B)Φ(A))=Lat(AB+BA), or Lat(Φ(A)Φ(B)Φ(A))=Lat(ABA), or Lat([Φ(A),Φ(B)])=Lat([A,B]).