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The $\mathbb{L}^ \bullet$-Homology fundamental class for singular spaces and the stratified Novikov conjecture

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Post-edited
Authors : Banagl, Markus (Author of the conference)
CIRM (Publisher )

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$\mathbb{L}$ fundamental class for manifolds intersection Poincaré spaces symmetric signature ad theories intersection Poincaré ads symmetric $\mathbb{L}$-spectra from IP-ads to L-ads $\mathbb{L}$-homology class characteristic L-classes Novikov higher signatures signature operator questions of the audience
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, Guillaume
    Language : 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 stratifiés
Event 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.19000503
Cite 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

Bibliography

  • Albin, P., Leichtnam, E., Mazzeo, R., & Piazza, P. (2013). The Novikov conjecture on Cheeger spaces. - https://arxiv.org/abs/1308.2844

  • Banagl, M., Laures, G., & McClure, J.E. (2014). The L-Homology Fundamental Class for IP-Spaces and the Stratified Novikov Conjecture. - http://arxiv.org/abs/1404.5395

  • 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


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