Topological Signal Processing by Michael Robinson

Author:Michael Robinson
Language: eng
Format: epub
Publisher: Springer Berlin Heidelberg, Berlin, Heidelberg

4.3.1 Orientation

Orientation of cells in a cell complex determines how information stored in a sheaf is tested for consistency. Suppose that is a sheaf on a cell complex in which and are attached to an edge , as shown in the diagram below

In order to extend a section that is supported on and to , we must have that

If is a sheaf of abelian groups , this equation can be written

or

This suggests that and should be assigned opposite signs. The concept of orientation makes this assignment precise.

We begin by defining the orientation of a nonsingular linear map between two vector spaces .

Definition 4.9

The orientation of a nonsingular linear map is the sign of its determinant.

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.