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McClure-Smith cosimplicial machinery and the cacti operad

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Paul Arnaud Songhafouo Tsopméné

Algebraic Topology · Submitted 28 Mar 2014

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Our main result says that they are compatible in the sense that some squares must commute.

how it is stated · asserted 0.98 read the record →

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arXiv ID1403.7504 (version 1)
Pith IDTX7TMIAZ, Pith's permanent record of this paper and its review
CitationPaul Arnaud Songhafouo Tsopm\'en\'e. "McClure-Smith cosimplicial machinery and the cacti operad." arXiv:1403.7504 (2014). https://pith.science/paper/TX7TMIAZ
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,829 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.07 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.80 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

McClure and Smith constructed a functor that sends a topological multiplicative operad O to an E_2 algebra TotO. They define in fact an operad D_2 (acting on the totalization TotO) weakly equivalent to the little 2-disks operad. On the other hand, Salvatore showed that D_2 is isomorphic to the cacti operad MS, which has a nice geometric description. He also built a geometric action of MS on TotO. In this paper we detail the McClure-Smith action and the cacti action. Our main result says that they are compatible in the sense that some squares must commute.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 McClure and Smith constructed a functor that sends a topological multiplicative operad O to an E_2 algebra TotO. background 1.00 0.04 0.02 asserted 1.00
s1 They define in fact an operad D_2 (acting on the totalization TotO) weakly equivalent to the little 2-disks operad. background 0.93 0.06 0.03 asserted 1.00
s2 On the other hand, Salvatore showed that D_2 is isomorphic to the cacti operad MS, which has a nice geometric description. background 1.00 0.03 0.02 asserted 1.00
s3 He also built a geometric action of MS on TotO. background 1.00 0.05 0.02 asserted 1.00
s4 In this paper we detail the McClure-Smith action and the cacti action. contribution 0.99 0.79 0.03 asserted 0.97
s5 Our main result says that they are compatible in the sense that some squares must commute. result 0.99 0.90 0.98 asserted 0.98

What kind of paper the classifier reports this is: theoretical result 0.99 · evidence from proof or derivation 0.81.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

McClure and Smith constructed a functor that sends a topological multiplicative operad O to an E_2 algebra TotO. They define in fact an operad D_2 (acting on the totalization TotO) weakly equivalent to the little 2-disks operad. On the other hand, Salvatore showed that D_2 is isomorphic to the cacti operad MS, which has a nice geometric description. He also built a geometric action of MS on TotO. In this paper we detail the McClure-Smith action and the cacti action. Our main result says that they are compatible in the sense that some squares must commute.

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