Explore BrainMass
Share

Explore BrainMass

    The Exact Homology Sequence (Exact Sequence of Triples)

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    Problem:

    Let X = X_1 / X_2, and A = X_1 / X_2. Using the exact sequence of triples, show that if the inclusion (X_1, A) --> (X, X_2) induces an isomorphism on homology, then the same holds for the inclusion (X_2, A) --> (X, X_1).

    Notation:
    X_1 is X subscript 1
    / is union
    / is intersection
    --> is an inclusion map
    H_q (X, A) is the quotient module, the qth relative homology module of X mod A

    Need a step-by-step proof outline.

    © BrainMass Inc. brainmass.com October 9, 2019, 5:00 pm ad1c9bdddf
    https://brainmass.com/math/algebra/exact-homology-sequence-exact-sequence-triples-45500

    Solution Summary

    This solution is comprised of a detailed explanation to provide a step-by-step proof outline.

    $2.19