arXiv Open Access 2001

An asymptotic dimension for metric spaces, and the 0-th Novikov-Shubin invariant

Daniele Guido Tommaso Isola

Lihat Sumber

Abstrak

A nonnegative number d_infinity, called asymptotic dimension, is associated with any metric space. Such number detects the asymptotic properties of the space (being zero on bounded metric spaces), fulfills the properties of a dimension, and is invariant under rough isometries. It is then shown that for a class of open manifolds with bounded geometry the asymptotic dimension coincides with the 0-th Novikov-Shubin number alpha_0 defined previously (math.OA/9802015, cf. also math.DG/0110294). Thus the dimensional interpretation of alpha_0 given in the mentioned paper in the framework of noncommutative geometry is established on metrics grounds. Since the asymptotic dimension of a covering manifold coincides with the polynomial growth of its covering group, the stated equality generalises to open manifolds a result by Varopoulos.

Topik & Kata Kunci

math.DG math.OA

Penulis (2)

Daniele Guido

Tommaso Isola

Format Sitasi

APA MLA BibTeX

Guido, D., Isola, T. (2001). An asymptotic dimension for metric spaces, and the 0-th Novikov-Shubin invariant. https://arxiv.org/abs/math/0110295

Akses Cepat

Lihat di Sumber

Informasi Jurnal

Tahun Terbit: 2001
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓