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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Spring 2015 • Question 7

Question

Math 6510 • Differentiable Manifolds Spring 2015 • Question 7

Regard the \(n\)-simplex \(\Delta ^n\) as a \(\Delta \)-complex in the natural way, with \((n+1)\) vertices and a single \(n\)-simplex. Find all subcomplexes \(X\subset \Delta ^n\) such that \(\operatorname {H}_{n-1}(X)\ne 0\) (with a proof that there are no others).

Raw LaTeX

Regard the \(n\)-simplex \(\Delta^n\) as a \(\Delta\)-complex in the natural way,
with \((n+1)\) vertices and a single \(n\)-simplex. Find all subcomplexes
\(X\subset\Delta^n\) such that \(\HH_{n-1}(X)\ne0\) (with a proof that there are no
others).

Topic Tags

Simplicial and Delta Complexes