Resolutions in dimension three
by
T.L. Thickstun
Southwest Texas State University

The speaker will survey the existing partial results on the Resolution Conjecture in dimension three(any generalized 3-manifold is the cell-like image of a 3-manifold). The most recent of these due to R.J. Daverman and the speaker (preprint in preparation) is of particular interest. It ensures resolvability (modulo the PC) if the generalized 3-manifold satisfies a relative version (RSAP) of the spherical simplicial approximation property of R.J. Daverman and D. Repovs. This resolution theorem together with the appropriate ``approximability'' theorem (also due to Daverman/Repovs) shows that(modulo PC) the RSAP detects 3-manifolds among generalized 3-manifolds.

Date received: June 18, 2001