Intrinsically (n − 2)-dimensional cellular decompositions of Eⁿ

Robert Jay Daverman and Dennis J. Garity

Vol. 102 (1982), No. 2, 275–283

DOI: 10.2140/pjm.1982.102.275

Abstract

Let G be a CE use decomposition of an n-manifold M. The intrinsic dimension of G is a measure of the minimal dimension of the image of the nondegeneracy set of CE maps from M onto M∕G which approximate the natural projection map. Examples of totally noncellular intrinsically n-dimensional decompositions of Eⁿ, n ≧ 3, are known to exist. Here it is shown that there also exist cellular decompositions of Eⁿ, n ≧ 3, which are intrinsically (n − 2)-dimensional.

Mathematical Subject Classification 2000

Primary: 57N12

Secondary: 54B15, 57N15

Milestones

Received: 7 November 1980

Revised: 5 August 1981

Published: 1 October 1982