Translation invariant asymptotic homomorphisms: equivalence of two approaches in the index theory
| dc.creator | Manuilov, V. | |
| dc.date | 2004-04-30 | |
| dc.date.accessioned | 2026-07-07T05:07:49Z | |
| dc.date.available | 2026-07-07T05:07:49Z | |
| dc.description | The algebra $Ψ(M)$ of order zero pseudodifferential operators on a compact manifold $M$ defines a well-known $C^*$-extension of the algebra $C(S^*M)$ of continuous functions on the cospherical bundle $S^*M\subset T^*M$ by the algebra $\K$ of compact operators. In his proof of the index theorem, Higson defined and used an asymptotic homomorphism $T$ from $C_0(T^*M)$ to $\K$, which plays the role of a deformation for the commutative algebra $C_0(T^*M)$. Similar constructions exist also for operators and symbols with coefficients in a $C^*$-algebra. We show that the image of the above extension under the Connes--Higson construction is $T$ and that this extension can be reconstructed out of $T$. This explains, why the classical approach to the index theory coincides with the one based on asymptotic homomorphisms. | |
| dc.description | 7 pages | |
| dc.identifier | https://arxiv.org/abs/math/0404546 | |
| dc.identifier | http://arxiv.org/abs/math/0404546 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71015 | |
| dc.subject | Operator Algebras | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 19K56; 46L80; 58J20 | |
| dc.title | Translation invariant asymptotic homomorphisms: equivalence of two approaches in the index theory | |
| dc.type | text |