Paper read at the Symposium on Categorical Algebra and Topology University of Cape Town 29 June—3 July 1981

CONES AND COMPARISONS IN IND-AFFINE HOMOTOPY THEORY

Published in: Quaestiones Mathematicae
Volume 6 , issue 1-3 , 1983 , pages: 49–66

DOI: 10.1080/16073606.1983.9632291

Author(s): Paul Cherenack Department of Mathematics,

Keywords: 14F35 , 14A20 , 14J15

Abstract

Ind-affine schemes over an algebraically closed field k are introduced. The cone functor is then defined and characterized in the based category (ind-aff)* of ind-affine schemes. Homotopy theories, one induced from the monad related to the cone functor and the other via unirational and then singular simplices, are compared. Some homotopy groups vis-a-vis (ind-aff)* taking as our model of the circle the set of points (x,y) in k² satisfying x²+y² = 1 are determined.

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