The L-homology fundamental class for IP-spaces and the stratified Novikov conjecture
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 ZZ{\mathbb {Z}...
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| Hauptverfasser: | , , |
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| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
| Veröffentlicht: |
06 February 2019
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Selecta mathematica
Year: 2019, Jahrgang: 25, Heft: 7, Pages: 1-104 |
| ISSN: | 1420-9020 |
| DOI: | 10.1007/s00029-019-0458-y |
| Online-Zugang: | Verlag, Volltext: https://doi.org/10.1007/s00029-019-0458-y
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| Verfasserangaben: | Markus Banagl, Gerd Laures, James E. McClure |
MARC
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| 520 | |a 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 ZZ{\mathbb {Z}}, which is, up to weak equivalence, an E∞E∞E_\infty 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. | ||
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| 650 | 4 | |a Bordism | |
| 650 | 4 | |a Characteristic classes | |
| 650 | 4 | |a Intersection homology | |
| 650 | 4 | |a L-theory | |
| 650 | 4 | |a Novikov conjecture | |
| 650 | 4 | |a pseudomanifolds | |
| 650 | 4 | |a Signature | |
| 650 | 4 | |a Stratified spaces | |
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