On the connection between the topological genus of certain polyhedra and the algebraic genus of their Hilton-Hopt quadratic forms.

Bokor, Imre. "On the connection between the topological genus of certain polyhedra and the algebraic genus of their Hilton-Hopt quadratic forms.." Publicacions Matemàtiques 34.2 (1990): 323-333. <http://eudml.org/doc/41140>.

@article{Bokor1990,
abstract = {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 simply connected differentiable 4-manifolds, the converse is also true, as long as the suspensions of the spaces are also of the same topological genus. This note allays the conjecture that the converse is true in general by offering two techniques for generating infinite families of counterexamples.},
author = {Bokor, Imre},
journal = {Publicacions Matemàtiques},
keywords = {Poliedro; Género; Formas cuadráticas; Hilton-Hopf invariant; cup product; cohomology; topological genus; algebraic genus; torsion subgroup; homotopy group},
language = {eng},
number = {2},
pages = {323-333},
title = {On the connection between the topological genus of certain polyhedra and the algebraic genus of their Hilton-Hopt quadratic forms.},
url = {http://eudml.org/doc/41140},
volume = {34},
year = {1990},
}

TY - JOUR
AU - Bokor, Imre
TI - On the connection between the topological genus of certain polyhedra and the algebraic genus of their Hilton-Hopt quadratic forms.
JO - Publicacions Matemàtiques
PY - 1990
VL - 34
IS - 2
SP - 323
EP - 333
AB - 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 simply connected differentiable 4-manifolds, the converse is also true, as long as the suspensions of the spaces are also of the same topological genus. This note allays the conjecture that the converse is true in general by offering two techniques for generating infinite families of counterexamples.
LA - eng
KW - Poliedro; Género; Formas cuadráticas; Hilton-Hopf invariant; cup product; cohomology; topological genus; algebraic genus; torsion subgroup; homotopy group
UR - http://eudml.org/doc/41140
ER -