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Homotopy theory, homological algebra, algebraic treatments of manifolds.

7 votes
2 answers
484 views

Does homotopy equivalence to a wedge of spheres imply shellability?

It's pretty clear that for a simplicial complex $\Delta$, shellability of the complex implies that it is homotopy equivalent to a wedge of spheres. However, does the converse hold? That is, does $\Del …