Français
The $\mathbb{L}^ \bullet$-Homology fundamental class for singular spaces and the stratified Novikov conjecture
Post-edited
Authors : Banagl, Markus (Author of the conference)
CIRM (Publisher )
19G24 - $L$-theory of group rings
55N33 - Intersection homology and cohomology
57N80 - Stratifications
57R20 - Characteristic classes and numbers
57R67 - Surgery obstructions, Wall groups
CIRM (Publisher )
Abstract :
An oriented manifold possesses an L-homology fundamental class which is an integral refinement of its Hirzebruch L-class and assembles to the symmetric signature. In joint work with Gerd Laures and James McClure, we give a construction of such an L-homology fundamental class for those oriented singular spaces, which are integral intersection homology Poincaré spaces. Our approach constructs a morphism of ad theories from intersection Poincaré bordism to L-theory. We shall indicate an application to the stratified Novikov conjecture. The latter has been treated analytically by Albin, Leichtnam, Mazzeo and Piazza.
MSC Codes : 19G24 - $L$-theory of group rings
55N33 - Intersection homology and cohomology
57N80 - Stratifications
57R20 - Characteristic classes and numbers
57R67 - Surgery obstructions, Wall groups
|
Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 01/07/16 Conference Date : 14/06/16 Subseries : Research talks arXiv category : Algebraic Topology Mathematical Area(s) : Topology Format : MP4 (.mp4) - HD Video Time : 00:54:24 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2016-06-14_Banagl.mp4 
|
Information on the Event
Event Title : Analysis, geometry and topology of stratified spaces / Analyse, géométrie et topologie des espaces stratifiésEvent Organizers : Mazzeo, Rafe ; Leichtnam, Eric ; Piazza, Paolo Dates : 13/06/16 - 17/06/16 Event Year : 2016 Event URL : http://conferences.cirm-math.fr/1422.html
Citation Data
DOI : 10.24350/CIRM.V.19000503Cite this video as: Banagl, Markus (2016). The $\mathbb{L}^ \bullet$-Homology fundamental class for singular spaces and the stratified Novikov conjecture. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19000503 URI : http://dx.doi.org/10.24350/CIRM.V.19000503 |
See Also
- [Multi angle] An Obata-Lichnerowicz theorem for stratified spaces / Author of the conference Mondello, Ilaria.
- [Multi angle] On the Hodge-Kodaira Laplacian on the canonical bundle of a compact Hermitian complex space / Author of the conference Bei, Francesco.
- [Multi angle] Extending the Cheeger-Müller theorem through degeneration / Author of the conference Albin, Pierre.
- [Multi angle] Analytic torsion for locally symmetric spaces of finite volume / Author of the conference Müller, Werner.
- [Multi angle] $L^2$-cohomology and the theory of weights / Author of the conference Saper, Leslie.
Bibliography
- Albin, P., Leichtnam, E., Mazzeo, R., & Piazza, P. (2013). The Novikov conjecture on Cheeger spaces.
- Banagl, M., Laures, G., & McClure, J.E. (2014). The L-Homology Fundamental Class for IP-Spaces and the Stratified Novikov Conjecture.
- Cappell, S., Shaneson, J., Weinberger, S. (1991). Classes topologiques caractéristiques pour les actions de groupes sur les espaces singuliers. Comptes Rendus de l'Académie des Sciences. Série I, 313(5), 293-295 - http://gallica.bnf.fr/ark:/12148/bpt6k57325582
