Goodwillie Approximations to Higher Categories.

Format:

Book

Author/Creator:

Heuts, Gijs.

Series:

Memoirs of the American Mathematical Society

Memoirs of the American Mathematical Society ; v.272

Language:

English

Subjects (All):

Homotopy groups.

Algebraic topology.

Spectral sequences (Mathematics).

Class field towers.

Physical Description:

1 online resource (126 pages)

Edition:

1st ed.

Place of Publication:

Providence : American Mathematical Society, 2021.

Summary:

"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 generally, we construct such a tower for a large class of -categories C and classify such Goodwillie towers in terms of the derivatives of the identity functor of C. As a 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"-- Provided by publisher.

Contents:

Main results

Constructing n-excisive approximations

Another construction of polynomial approximations

Coalgebras in stable [infinity]-operads

The space of Goodwillie towers

Examples.

Notes:

Description based on publisher supplied metadata and other sources.

"July 2021, volume 272, number 1333 (third of 7 numbers)."

Includes bibliographical references.

ISBN:

9781470467494

1470467496

OCLC:

1275392905