# Degree of a Map

1. Oct 20, 2008

### jimisrv

Hi,

I am having some problems understanding the degree of a continuous map g:circle --> circle

I have found a definition in Munkres (pg 367) that I can't really understand (I'm an engineering student with little algebraic topology) and one in Lawson (pg 181), Topology:A Geometric approach, that makes some sense.

Lawson defines it:

For g as above, consider p : I --> circle and a lift h:I --> R
such that gp=ph

Then define the degree of g as

deg g =h(1)-h(2)

Intuitively I understand this to be the integer number of times the image of the circle wraps around the circle under g? If so, what about the continuous function g(x)=exp(i*pi*x/2) where x is in[0,2pi). The image would only wrap around half the circle, which would be homotopic to the constant map, a map of degree 0...but according to the above definition this would have degree 1/2?

Thanks for any help!

Regards,
Mike

Last edited: Oct 20, 2008
2. Oct 21, 2008