Reducibility of low-dimensional Poincare duality spaces

Land, Markus (2022): Reducibility of low-dimensional Poincare duality spaces. In: Münster Journal of Mathematics, Bd. 15, Nr. 1: S. 47-81

Abstract

We discuss Poincare duality complexes X and the question whether or not their Spivak normal fibration admits a reduction to a vector bundle in the case where the dimension of X is at most 4. We show that in dimensions less than 4 such a reduction always exists, and in dimension 4 such a reduction exists provided X is orientable. In the non-orientable case, there are counterexamples to reducibility by Hambleton-Milgram.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Mathematik, Informatik und Statistik > Mathematik
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik
• ISSN: Mathematisches Institut (Universität Münster)
• Sprache: Englisch
• DFG: Gefördert durch die Deutsche Forschungsgemeinschaft (DFG) - 224262486