Author 1: John Maginnis Address: Mathematics Department, Kansas State University, 137 Cardwell Hall, Manhattan, Kansas 66506 Author 2: Silvia Onofrei Address: Mathematics Department, University of California Riverside, 226 Surge Hall, Riverside, California 92521 Title: On a homotopy relation between the 2-local geometry and the Bouc complex for the sporadic group Co3 Abstract: We study the homotopy relation between the standard 2-local geometry and the Bouc complex for the sporadic group Co3. We also give a result concerning the relative projectivity of the reduced Lefschetz module associated to this 2-local geometry. Preprint, November 1, 2004