The aim of this paper is to prove a generalization of the famous Theorem A of Quillen for strict ∞-categories. This result is central to the homotopy theory of strict ∞-categories developed by the authors. The proof presented here is of a simplicial nature and uses Steiner's theory of augmented directed complexes. In a subsequent paper, we will prove the same result by purely ∞-categorical methods. [ABSTRACT FROM AUTHOR]
*FIXED point theory, *POLYHEDRA, *EULER characteristic, *ABELIAN groups
Abstract
In 1969 R.H. Bing asked the following question: Is there a compact two-dimensional polyhedron with the fixed point property which has even Euler characteristic? In this paper we prove that there are no spaces with these properties and abelian fundamental group. We also show that the fundamental group of such a complex cannot have trivial Schur multiplier. [ABSTRACT FROM AUTHOR]