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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.
Göppl, Florian 1 ; Weiss, Michael 1
@article{10_2140_agt_2024_24_1655,
author = {G\"oppl, Florian and Weiss, Michael},
title = {A spectral sequence for spaces of maps between operads},
journal = {Algebraic and Geometric Topology},
pages = {1655--1690},
publisher = {mathdoc},
volume = {24},
number = {3},
year = {2024},
doi = {10.2140/agt.2024.24.1655},
url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2024.24.1655/}
}
TY - JOUR AU - Göppl, Florian AU - Weiss, Michael TI - A spectral sequence for spaces of maps between operads JO - Algebraic and Geometric Topology PY - 2024 SP - 1655 EP - 1690 VL - 24 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.2140/agt.2024.24.1655/ DO - 10.2140/agt.2024.24.1655 ID - 10_2140_agt_2024_24_1655 ER -
%0 Journal Article %A Göppl, Florian %A Weiss, Michael %T A spectral sequence for spaces of maps between operads %J Algebraic and Geometric Topology %D 2024 %P 1655-1690 %V 24 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.2140/agt.2024.24.1655/ %R 10.2140/agt.2024.24.1655 %F 10_2140_agt_2024_24_1655
Göppl, Florian; Weiss, Michael. A spectral sequence for spaces of maps between operads. Algebraic and Geometric Topology, Tome 24 (2024) no. 3, pp. 1655-1690. doi: 10.2140/agt.2024.24.1655
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