The complex of partial bases of a free group

27 Nov 2017  ·  Costa Iván Sadofschi ·

We prove that the simplicial complex whose simplices are the nonempty partial bases of $\mathbb{F}_n$ is homotopy equivalent to a wedge of $(n-1)$-spheres. Moreover, we show that it is Cohen-Macaulay...

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Algebraic Topology