Download this article
 Download this article For screen
For printing
Recent Issues

Volume 24
Issue 3, 1225–1808
Issue 2, 595–1223
Issue 1, 1–594

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
 
Other MSP Journals
A spectral sequence for spaces of maps between operads

Florian Göppl and Michael Weiss

Algebraic & Geometric Topology 24 (2024) 1655–1690
Abstract

Under mild conditions on topologically enriched operads P and Q, the derived mapping space RHom (P,Q) is the limit (sequential homotopy inverse limit) of a tower whose n th layer admits a description in terms of certain (small) diagrams Jn(P) and Jn(Q). More precisely Jn(P) is a 3–term diagram of spaces with action of Σn of the form bound n(P) P(n) cobound n(P), where P(n) is the space of n–ary operations in P. The statement takes some inspiration from manifold calculus, but the proof relies on the homotopical theory of dendroidal spaces and the concept of dendroidal nerve of an operad.

Keywords
operad, dendroidal space, spectral sequence
Mathematical Subject Classification
Primary: 18M75, 55P48
Secondary: 18N60
References
Publication
Received: 15 June 2022
Revised: 23 October 2022
Accepted: 18 November 2022
Published: 28 June 2024
Authors
Florian Göppl
Mathematics Institute
University of Münster
Frankfurt
Germany
Michael Weiss
Mathematics Institute
University of Münster
Frankfurt
Germany

Open Access made possible by participating institutions via Subscribe to Open.