Pith. Sign in

RECORD

Free Loop Spaces and Cyclohedra

PaperPDF from arXiv

data files

Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
X Bluesky LinkedIn Reddit Hacker News
Martin Markl

Algebraic Topology · Submitted 22 Mar 2002

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

The authors' main claim We will then discuss how this action can be used for an appropriate recognition principle in the same manner as the action of Stasheff's associahedra can be used to recognize based loop spaces.

how it is stated · hedged possibility 0.57 read the record →

Comment (0) Read on arXiv ↗
Cite ▾
arXiv IDmath/0203236 (version 1)
Pith IDZQ3F3273, Pith's permanent record of this paper and its review
CitationMartin Markl. "Free Loop Spaces and Cyclohedra." arXiv:math/0203236 (2002). https://pith.science/paper/ZQ3F3273
Claim paper

The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Open the compiled record

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,495 input tokens.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.07 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.90 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

In this note we introduce an action of cyclohedra on the free loop space. We will then discuss how this action can be used for an appropriate recognition principle in the same manner as the action of Stasheff's associahedra can be used to recognize based loop spaces. We will also interpret one result of R.L. Cohen as an approximation theorem, in the spirit of Beck and May, for free loop spaces.

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 In this note we introduce an action of cyclohedra on the free loop space. contribution 1.00 0.94 0.34 asserted 1.00
s1 We will then discuss how this action can be used for an appropriate recognition principle in the same manner as the action of Stasheff's associahedra can be used to recognize based loop spaces. contribution 0.67 0.49 0.37 hedged possibility 0.57
s2 We will also interpret one result of R.L. contribution 0.50 0.53 0.05 asserted 0.61
s3 Cohen as an approximation theorem, in the spirit of Beck and May, for free loop spaces. interpretation 0.94 0.56 0.13 asserted 0.94

What kind of paper the classifier reports this is: theoretical result 0.72 · evidence from proof or derivation 0.85.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

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

In this note we introduce an action of cyclohedra on the free loop space. We will then discuss how this action can be used for an appropriate recognition principle in the same manner as the action of Stasheff's associahedra can be used to recognize based loop spaces. We will also interpret one result of R.L. Cohen as an approximation theorem, in the spirit of Beck and May, for free loop spaces.

Human review

How Pith checks papers → · Full audit of this paper →

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.