Suppose that and are two oriented differentiable manifolds of dimension (without boundary) with compact and connected and suppose that is a differentiable mapping. Let denote the differential mapping at the point , that is the linear mapping . Let denote the sign of the determinant of . That is the sign is positive if preserves orientation and negative if reverses orientation.
Let be a regular value, then we define the Brower degree (or just degree) of by
It can be shown that the degree does not depend on the regular value that we pick so that is well defined.
Note that this degree coincides with the degree (http://planetmath.org/Degree5) as defined for maps of spheres.
- 1 John W. Milnor. . The University Press of Virginia, Charlottesville, Virginia, 1969.
|Date of creation||2013-03-22 14:52:37|
|Last modified on||2013-03-22 14:52:37|
|Last modified by||jirka (4157)|