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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6520 • Algebraic Topology

Fall 2024 • Question 2

Question

Math 6520 • Algebraic Topology Fall 2024 • Question 2

Suppose that a complex \(X\) is the union of two subcomplexes \(A\) and \(B\) with \(A\), \(B\), and \(A \cap B\) contractible. Prove that \(X\) is contractible.

Raw LaTeX

Suppose that a complex \(X\) is the union of two subcomplexes \(A\) and \(B\) with \(A\), \(B\), and \(A \cap B\)
contractible. Prove that \(X\) is contractible.

Topic Tags

Homotopy Equivalence, Retracts, and Contractibility Simplicial and Delta Complexes