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6 votes
2 answers
595 views

Graphs of maps between manifolds as cycles and intersection theory

I'm guessing that the answer to this question is well-known, but I'm struggling to find anything to help me. Let $X,Y$ be compact manifolds of dimension $n,m$ respectively. Let $f:X \to Y$ be a ...
8 votes
1 answer
2k views

What is the relation between Lefschetz fixed point theorem and Poincare-Hopf theorem on vector fields?

In Dubrovin/Fomenko/Novikov Modern geometry--Methods and applications, Part II, the (Poincare-)Hopf theorem is treated in section 15.2 (see theorem 15.2.7 on page 129), while the Lefschetz theorem on ...