Hi,(adsbygoogle = window.adsbygoogle || []).push({});

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

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Degree of a Map

**Physics Forums | Science Articles, Homework Help, Discussion**