Skip to content

Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 1994 • Question 8

Question

Math 6510 • Differentiable Manifolds Fall 1994 • Question 8

Let \(\{C_n,d_n\}\) and \(\{C'_n,d'_n\}\) be chain complexes of abelian groups and \(f_n:C_n\to C'_n\) be a chain homotopy equivalence. Then the induced map \(f_{n*}:H_n(C)\to H_n(C')\) is isomorphism in homology.

Raw LaTeX

Let \(\{C_n,d_n\}\) and \(\{C'_n,d'_n\}\) be chain complexes of
abelian groups and \(f_n:C_n\to C'_n\) be a chain homotopy equivalence. Then the
induced map \(f_{n*}:H_n(C)\to H_n(C')\) is isomorphism in homology.

Topic Tags

Chain Complexes and Chain Homotopy Homology with Coefficients Homotopy Equivalence, Retracts, and Contractibility Homotopy and Degree on Manifolds