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I'm reading a paper by Claude LeBrun about exotic smoothness on manifolds and he is talking about a connection between polynomials and groups that I am not familiar with (or at least I think that's what he's talking about). He's creating a line bundle (which happens to be O(2)) over the complex projective space CP^2 and he states that the "elements n of the line bundle are degree 2" (not actually a direct quote, but I'm almost positive that's what he's trying to say). So what this says to me is that there is some connection between the degree 2 polynomials (like p(x)=a+b*x + c*x^2) and the group of all 2x2 orthogonal matricies. I've been running this around in my head for a few days and I can't come up with a good explanation, so could someone help me out?

Thanks so much!

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# Connection between polynomials and groups

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