Direct application of the boundary theorem

Reference no: EM13724505

Prove the deg_2(f) is well defined by direct application of the Boundary Theorem. Note f is a smooth map of a compact manifold X into a connected manifold Y and dim X = dim Y. (Hint: if y_0, and y_1 in Y, alter f homotopically to get f traverses {y_0, y_1}). Not let c: I -> Y be a curve with c(0) = y_0, c(1) = y_1, and define F: X * I -> Y * Y by f * c. Examine the map df.

Reference no: EM13724505

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