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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Spring 2011 • Question 7

Question

Math 6510 • Differentiable Manifolds Spring 2011 • Question 7

An algebraic fact, often used in homology theory, is that a short exact sequence of chain complexes induces a long exact sequence in homology. State this fact carefully and give a definition of the “connecting homomorphism” (the one that lowers the degree of the homology group).

Raw LaTeX

An algebraic fact, often used in homology theory, is that a short exact
sequence of chain complexes induces a long exact sequence in homology. State
this fact carefully and give a definition of the ``connecting homomorphism''
(the one that lowers the degree of the homology group).

Topic Tags

Chain Complexes and Chain Homotopy Homology with Coefficients Lie Group Actions and Homomorphisms Relative Homology and Long Exact Sequences