.oooO Jim Stasheff jds@math.unc.edu (UNC) Math-UNC (919)-962-9607 \ ( Chapel Hill NC FAX:(919)-962-2568 \*) 27599-3250 http://www.math.unc.edu/Faculty/jds ---------- Forwarded message ---------- Date: Fri, 28 Jan 2000 12:26:36 EST From: DON DAVIS <dmd1@lehigh.edu> To: toplist <Distribution.List@lehigh.edu> Subject: 2 on terminology Two similar responses regarding simplicial terminology.....DMD ______________________________________________________ Date: Fri, 28 Jan 2000 08:56:36 -0600 (CST) From: Peter May <may@math.uchicago.edu> Subject: "Delta sets" Once upon a time, people doing category theory and algebraic topology overlapped with people doing geometric topology and algebraic topology. There is a large literature of $\triangle$-sets, or $\delta$-sets, which are precisely simplicial sets without degeneracy operations. I believe the term was introduced in the pair of papers listed in MathSciNet as "$\triangle$-sets. I II", by Colin Rourke and Brian Sanderson. Both papers were published in 1971, in the Quarterly Journal of Mathematics. The main point is that use of delta sets is essential to the theory of block bundles and thus to PL topology. Peter May ______________________________________________________________ Date: Fri, 28 Jan 2000 15:12:58 GMT From: Brian Sanderson <bjs@maths.warwick.ac.uk> Subject: Re: terminology. Delta sets. J. Stasheff wrote:
Has terminology settled down? I can recall seeing various terms for ``simplicial object without degeneracies''
Colin Rourke and I called these sets Delta sets. Unfortunately you might have to look for "$\triangle" to find them. Prior to the two papers below they were a neglected curiosity. We needed them when block bundles emerged. I don't know how current the terminology is now. Brian Sanderson [7] 45 #9328 Rourke, C. P.; Sanderson, B. J. $\triangle $-sets. II. Block bundles and block fibrations. Quart. J. Math. Oxford Ser. (2) 22 (1971), 465--48 5. (Reviewer: E. B. Curtis) 55F60 [8] 45 #9327 Rourke, C. P.; Sanderson, B. J. $\triangle $-sets. I. Homotopy theory. Quart. J. Math. Oxford Ser. (2) 22 (1971), 321--338. (Reviewer: E. B. Curtis) 55F60 (55D99)