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}...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article (Journal) |
| Language: | English |
| Published: |
06 February 2019
|
| In: |
Selecta mathematica
Year: 2019, Volume: 25, Issue: 7, Pages: 1-104 |
| ISSN: | 1420-9020 |
| DOI: | 10.1007/s00029-019-0458-y |
| Online Access: | Verlag, Volltext: https://doi.org/10.1007/s00029-019-0458-y
|
| Author Notes: | Markus Banagl, Gerd Laures, James E. McClure |
| Summary: | 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. |
|---|---|
| Item Description: | Gesehen am 22.08.2019 |
| Physical Description: | Online Resource |
| ISSN: | 1420-9020 |
| DOI: | 10.1007/s00029-019-0458-y |