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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Spring 2012 • Question 10

Question

Math 6510 • Differentiable Manifolds Spring 2012 • Question 10

Let \(X\) be a topological space and \(A\subset X\) a subspace. Define relative homology \(H_k(X,A)\) and the boundary homomorphism \(H_k(X,A)\to H_{k-1}(A)\).

Raw LaTeX

Let \(X\) be a topological space and \(A\subset X\) a subspace. Define relative
homology \(H_k(X,A)\) and the boundary homomorphism \(H_k(X,A)\to H_{k-1}(A)\).

Topic Tags

Homology with Coefficients Lie Group Actions and Homomorphisms Point-Set Topology and Separation Theorems Relative Homology and Long Exact Sequences