Reducibility of low-dimensional Poincare duality spaces

Land, Markus (2022): Reducibility of low-dimensional Poincare duality spaces. In: Münster Journal of Mathematics, Vol. 15, No. 1: pp. 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.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics
• Subjects: 500 Science > 510 Mathematics
• ISSN: Mathematisches Institut (Universität Münster)
• Language: English
• DFG: Gefördert durch die Deutsche Forschungsgemeinschaft (DFG) - 224262486