Goodwillie Approximations to Higher Categories: 272 (Memoirs of the American Mathematical Society) - Softcover

Gijs Heuts (author)

Softcover

ISBN 10: 1470448939 ISBN 13: 9781470448936

Publisher: American Mathematical Society, 2022

Synopsis

We construct a Goodwillie tower of categories which interpolates between the category of pointed spaces and the category of spectra. This tower of categories refines the Goodwillie tower of the identity functor in a precise sense. More gen-erally, we construct such a tower for a large class of ?-categories C and classify such Goodwillie towers in terms of thederivatives of the identity functor of C.Asa particular application we show how this provides a model for the homotopy theory of simply-connected spaces in terms of coalgebras in spectra with Tate diagonals. Our classification of Goodwillie towers simplifies considerably in settings where the Tate cohomology of the symmetric groups vanishes. As an example we apply our methods to rational homotopy theory. Another application identifies the homotopy theory of p-local spaces with homotopy groups in a certain finite range with the homotopy theory of certain algebras over Ching's spectral version of the Lie operad. This is a close analogue of Quillen's results on rational homotopy.

About this title

About the Author

Gijs Heuts, University of Copenhagen, Denmark.

Edition details

• Publisher: American Mathematical Society
• Publication date: 2022
• Language: English
• ISBN 10: 1470448939
• ISBN 13: 9781470448936
• Binding: Paperback
• Number of pages: 277