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  • Title
    Reducibility of low-dimensional Poincaré duality spaces
  • Author
    Land, Markus
  • Is part of
    Münster Journal of Mathematics, Issue Münster Journal of Mathematics, page 47-81
  • Published
    2022
  • Annotation
    Förderer: Deutsche Forschungsgemeinschaft / Projektnummer: CRC 1085
    Funding organisation: Deutsche Forschungsgemeinschaft / Project number: CRC 1085
    Förderer: Danish National Research Foundation / Projektnummer: DNRF151
    Funding organisation: Danish National Research Foundation / Project number: DNRF151
  • Language
    English
  • Document type
    Journal Article
  • URN
    urn:nbn:de:hbz:6-23049551583 
  • DOI
    10.17879/23049551069 
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Abstract
  • We discuss Poincaré 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.
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