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Record W2149181791 · doi:10.1090/gsm/176

Ordered Groups and Topology

2016· book· en· W2149181791 on OpenAlex

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.

Bibliographic record

VenueGraduate studies in mathematics · 2016
Typebook
Languageen
FieldMathematics
TopicGeometric and Algebraic Topology
Canadian institutionsUniversity of British ColumbiaUniversity of Manitoba
Fundersnot available
KeywordsMathematicsBraid groupKnot (papermaking)Betti numberAlgebraic numberSingular homologyGroup (periodic table)Fundamental groupBraid theoryHomology (biology)Floer homologyPure mathematicsTopology (electrical circuits)Combinatorics

Abstract

fetched live from OpenAlex

This book deals with the connections between topology and ordered groups. It begins with a self-contained introduction to orderable groups and from there explores the interactions between orderability and objects in low-dimensional topology, such as knot theory, braid groups, and 3-manifolds, as well as groups of homeomorphisms and other topological structures. The book also addresses recent applications of orderability in the studies of codimension-one foliations and Heegaard-Floer homology. The use of topological methods in proving algebraic results is another feature of the book. The book was written to serve both as a textbook for graduate students, containing many exercises, and as a reference for researchers in topology, algebra, and dynamical systems. A basic background in group theory and topology is the only prerequisite for the reader.

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

Full frame distilled prediction

Teacher imitation

Not calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.

metaresearch head score (Codex)0.001
metaresearch head score (Gemma)0.003
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesMeta-epidemiology (narrow)
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Other · Consensus signal: Other
Teacher disagreement score0.121
Threshold uncertainty score1.000

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0010.003
Meta-epidemiology (narrow)0.0010.000
Meta-epidemiology (broad)0.0020.000
Bibliometrics0.0010.000
Science and technology studies0.0000.001
Scholarly communication0.0000.000
Open science0.0000.001
Research integrity0.0000.001
Insufficient payload (model declined to judge)0.0000.000

Machine scores (provisional)

The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.

Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.

Opus teacher head0.192
GPT teacher head0.373
Teacher spread0.181 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it