The Atiyah Patodi Singer signature formula for measured foliations
| dc.creator | Antonini, Paolo | |
| dc.date | 2009-01-02 | |
| dc.date | 2009-01-06 | |
| dc.date.accessioned | 2026-07-07T12:24:28Z | |
| dc.date.available | 2026-07-07T12:24:28Z | |
| dc.description | Let $(X_0,\mathcal{F}_0) $ be a compact manifold with boundary endowed with a foliation $\mathcal{F}_0$ which is assumed to be measured and transverse to the boundary. We denote by $Λ$ a holonomy invariant transverse measure on $(X_0,\mathcal{F}_0) $ and by $\mathcal{R}_0$ the equivalence relation of the foliation. Let $(X,\mathcal{F})$ be the corresponding manifold with cylindrical end and extended foliation with equivalence relation $\mathcal{R}$. In the first part of this work we prove a formula for the $L^2$-$Λ$ index of a longitudinal Dirac-type operator $D^{\mathcal{F}}$ on $X$ in the spirit of Alain Connes' non commutative geometry $ind_{L^2,Λ}(D^{\mathcal{F},+}) = <\hat{A}(T\mathcal{F})Ch(E/S),C_Λ> + 1/2[η_Λ(D^{\mathcal{F}_\partial}) - h^+_Λ + h^-_Λ].$ | |
| dc.description | Ph.D Thesis, La Sapienza Rome | |
| dc.identifier | https://arxiv.org/abs/0901.0143 | |
| dc.identifier | http://arxiv.org/abs/0901.0143 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/214333 | |
| dc.subject | Differential Geometry | |
| dc.title | The Atiyah Patodi Singer signature formula for measured foliations | |
| dc.type | text |