The L-homology fundamental class for IP-spaces and the stratified Novikov conjecture

• Markus Banagl ^[3] ; Gerd Laures ^[1] ; James E. McClure ^[2]
  1. [1] Ruhr University Bochum

     Ruhr University Bochum

     Kreisfreie Stadt Bochum, Alemania

     
  2. [2] Purdue University

     Purdue University

     Township of Wabash, Estados Unidos

     
  3. [3] Universität Heidelberg, Alemania

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• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 25, Nº. 1, 2019
• Idioma: inglés
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• Resumen

  • An IP-space is a pseudomanifold whose defining local properties imply that its middle perversity global intersection homology groups satisfy Poincaré duality integrally. We show that the symmetric signature induces a map of Quinn spectra from IP bordism to the symmetric L-spectrum of Z , which is, up to weak equivalence, an E∞ ring map. Using this map, we construct a fundamental L-homology class for IP-spaces, and as a consequence we prove the stratified Novikov conjecture for IP-spaces whose fundamental group satisfies the Novikov conjecture.