Imre Bokor

University of New England (Australia) | UNE · Mathematics (School of Science and Technology)

Turaev conjectured that the classification, realization and splitting results for Poincar\'e duality complexes of dimension $3$ (PD$_{3}$-complexes) generalize to PD$_{n}$-complexes with $(n-2)$-connected universal cover for $n \ge 3$. Baues and Bleile showed that such complexes are classified, up to oriented homotopy equivalence, by the triple con...

Baues and Bleille showed that, up to oriented homotopy equivalence, a Poincare duality complex of dimension $n \ge 3$ with $(n-2)$-connected universal cover, is classified by its fundamental group, orientation class and the image of its fundamental class in the homology of the fundamental group. We generalise Turaev's results for the case $n=3$, by...

It is commonly held that what distinguishes modern mathematics is the availability of high-speed electronic computers and pocket calculators with graphical capabilities. Consequently, mathematics is usually taught in schools and undergraduate courses as if Euler and Gauss were our contemporaries, with electronic gadgets replacing tables, slide-rule...

Without Abstract

The genus of the mapping cone C f of a map f:S m-1 →⋁S n (m>n>1) representing a suspension element of finite order in π m-1 (⋁S n ) is classified by a subgroup G f of π m-1 (S n ) depending only on the homotopy type of C f . The group G f finds application in proving that the genus of C f is trivial whenever C f has sufficiently many n-cells, the n...

Thegenus is determined for spaces of the homotopy type of aCW complex with one cell each in dimensions 0, 2n and 4n (and no other cells), such spaces providing the only cases of spaces with two non-trivial cells such that the homotopy class of the attaching map for the top cell is of infinite order and the genus of the space is non-trivial. The gen...

The Hilton-Hopf quadratic form is defined for spaces of the homotopy type of a CW complex with one cell each in dimensions 0 and 4n, K cells in dimension 2n and no other cells. If two such spaces are of the same topological genus, then their Hilton-Hopf quadratic forms are of the same weak algebraic genus. For large classes of spaces, such as simpl...