Date: Sun, 7 Feb 1999 15:46:29 -0800 (PST)
From: Sadok Kallel <skallel@math.ubc.ca>
Subject: Re: 2 questions

> Date: Sun, 7 Feb 1999 16:55:08 -0500 (EST)
> From: Dev Sinha <dps@math.brown.edu>
> Subject: Dold-Thom
>
> I have a simple question for the list.  Does anyone have a (favorite)
> explicit map from S^2 to SP^\infty T which represents a generator of
> H_2(T), where T is the torus?  Feel free to use the free abelian group on
> T instead of SP^\infty T.
>
> Thanks,
> Dev


The inclusion T--->SP^2T factors through the cofiber S^2 of the inclusion
of the 1-skeleton into T (this follows from the fact that the fundamental
group of SP^n, n>1 is abelian). The construction and some applications are
given in "divisor spaces on Riemann surfaces", Trans. Am. Math. Soc. 350
(1998), 135--164  (\S1.1). A detailed discussion of the geometry of this
spherical class with applications to the theory of curves can be obtained
from me in preprint form.

S. Kallel.
Dept. of Math, UBC.