On T. Petrie’s problem concerning homology planes

Floer Homology and Homotopy Planes

We compute the Floer homology of a certain family of homology 3spheres occuring as the boundary of a compactification of complex homotopy planes. The Floer complex turns out to be concentrated in even degrees and 2-periodic. This is proved by using suitable bordisms to Seifert fibred spaces.

Concerning maximal arcs and inversive planes

On the Construction of Finite Projective Planes from Homology Semibiplanes

From a projective plane Π with involutory homology τ one constructs an incidence system Π/τ having as points and blocks the 〈τ〉-orbits of length 2 on the points and lines of Π, and with incidence inherited from Π. Such incidence systems satisfy certain properties which, when taken as axioms, define the class of homology semibiplanes. We describe how one determines, in principle, whether a given...

Affine Lines on Q-homology Planes and Group Actions

This note is a supplement to the papers [KiKo] and [GMMR]. We show the role of group actions in classification of affine lines on Q-homology planes.

On a Problem concerning Permutation Polynomials

Let S(f) denote the set of integral ideals / such that / is a permutation polynomial modulo i", where / is a polynomial over the ring of integers of an algebraic number field. We obtain a classification for the sets S which may be written in the form S(f). Introduction. A polynomial f(x) with coefficients in a commutative ring R is said to be a permutation polynomial modulo an ideal I oi R (abb...