Volume 7, issue 2 (2003)

Download this article
For printing
Recent Issues

Volume 18
Issue 4, 1865–2486
Issue 3, 1245–1863
Issue 2, 617–1244
Issue 1, 1–616

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Author Index
Editorial procedure
Submission Guidelines
Submission Page
Author copyright form
Subscriptions
Contacts
G&T Publications
GTP Author Index
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Calculus III: Taylor Series

Thomas G Goodwillie

Geometry & Topology 7 (2003) 645–711

arXiv: math.AT/0310481

Abstract

We study functors from spaces to spaces or spectra that preserve weak homotopy equivalences. For each such functor we construct a universal n–excisive approximation, which may be thought of as its n–excisive part. Homogeneous functors, meaning n–excisive functors with trivial (n 1)–excisive part, can be classified: they correspond to symmetric functors of n variables that are reduced and 1–excisive in each variable. We discuss some important examples, including the identity functor and Waldhausen’s algebraic K–theory.

Keywords
Homotopy functor, excision, Taylor tower
Mathematical Subject Classification 2000
Secondary: 55U99
References
Forward citations
Publication
Received: 8 November 2002
Accepted: 20 October 2003
Published: 28 October 2003
Proposed: Haynes Miller
Seconded: Ralph Cohen, Gunnar Carlsson
Authors
Thomas G Goodwillie
Department of Mathematics
Brown University
Box 1917
Providence
Rhode Island 02912–0001
USA