Metadata
bibkey: ehrenborghetyei2006independence
authors: Richard Ehrenborg and Gábor Hetyei
year: 2006
title: The topology of the independence complex
doi: 10.1016/j.ejc.2005.04.010
claim: The independence complex of a finite forest is contractible or homotopy equivalent to a sphere, with empty realization treated separately.
strata_touched:
- D5/S3/Geometry/FiniteForestIndependence
license: citation-only
triage: anchor
Verified locator
DOI: 10.1016/j.ejc.2005.04.010. European Journal of Combinatorics 27 (2006), 906–923, Corollary 6.1.
Correspondence
The forest classification is classical. The Lean construction uses nonempty independent faces and their actual barycentric-coordinate realizations. Empty vertex types form a separate case; an empty residual in leaf reduction gives the two-point sphere through the augmented simplicial join. For a nonempty residual, the ordinary join transports the contractible or spherical outcome. The statement includes disconnected forests and the zero-sphere. It does not specify a modulo-three formula for the dimension of a path.