Classical and noncommutative geometry

Authors

Debashish Goswami, Indian Statistical Institute, Kolkata
Jyotishman Bhowmick, Indian Statistical Institute, Kolkata

Document Type

Book Chapter

Publication Title

Infosys Science Foundation Series in Mathematical Sciences

Abstract

We discuss classical Riemannian geometry and its noncommutative geometric counterparts. At first the definition and properties of the Hodge Laplacian and the Dirac operator are given. We also derive the characterizations of isometries (resp. orientation preserving isometries) in terms of the Laplacian (resp. Dirac operator). This is followed by discussion on noncommutative manifolds given by spectral triples, including the definitions of noncommutative space of forms and the Laplacian in this set up. The last section of this chapter deals with the quantum group equivariance in noncommutative geometry where we discuss some natural examples of equivariant spectral triples on the Podles’ spheres.

First Page

37

Last Page

67

DOI

10.1007/978-81-322-3667-2_2

Publication Date

1-1-2016

Recommended Citation

Goswami, Debashish and Bhowmick, Jyotishman, "Classical and noncommutative geometry" (2016). Book Chapters. 226.
https://digitalcommons.isical.ac.in/book-chapters/226