Pith. Sign in

RECORD

Connected components of strata of Abelian differentials over Teichm\"uller space

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
Aaron Calderon

Geometric Topology · Submitted 16 Jan 2019

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

The authors' main claim Unlike the case for unmarked Riemann surfaces, we find there can be many connected components, distinguished by roots of the cotangent bundle of the surface.

how it is stated · asserted 0.97 read the record →

Comment (0) Read on arXiv ↗
Cite ▾
arXiv ID1901.05482 (version 3)
Pith IDOJFK7SYY, Pith's permanent record of this paper and its review
CitationAaron Calderon. "Connected components of strata of Abelian differentials over Teichm\"uller space." arXiv:1901.05482 (2019). https://pith.science/paper/OJFK7SYY
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, 3,583 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.13 · human participants 0.01 · controlled comparison 0.09 · randomized assignment 0.01 · states quantitative result 0.07 · compares with prior results 0.80 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; .

This paper describes connected components of the strata of holomorphic abelian differentials on marked Riemann surfaces with prescribed degrees of zeros. Unlike the case for unmarked Riemann surfaces, we find there can be many connected components, distinguished by roots of the cotangent bundle of the surface. In the course of our investigation we also characterize the images of the fundamental groups of strata inside of the mapping class group. The main techniques of proof are mod r winding numbers and a mapping class group-theoretic analogue of the Euclidean algorithm.

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 This paper describes connected components of the strata of holomorphic abelian differentials on marked Riemann surfaces with prescribed degrees of zeros. contribution 0.92 0.89 0.55 asserted 0.99
s1 Unlike the case for unmarked Riemann surfaces, we find there can be many connected components, distinguished by roots of the cotangent bundle of the surface. result 0.99 0.94 0.46 asserted 0.97
s2 In the course of our investigation we also characterize the images of the fundamental groups of strata inside of the mapping class group. result 0.59 0.94 0.07 asserted 1.00
s3 The main techniques of proof are mod r winding numbers and a mapping class group-theoretic analogue of the Euclidean algorithm. method 1.00 0.86 0.04 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read
  • arXiv listing abstract v3
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

This paper describes connected components of the strata of holomorphic abelian differentials on marked Riemann surfaces with prescribed degrees of zeros. Unlike the case for unmarked Riemann surfaces, we find there can be many connected components, distinguished by roots of the cotangent bundle of the surface. In the course of our investigation we also characterize the images of the fundamental groups of strata inside of the mapping class group. The main techniques of proof are mod r winding numbers and a mapping class group-theoretic analogue of the Euclidean algorithm.

Human review

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

How the literature uses it

What this paper does with the arXiv papers it cites

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

What it cites · 8 sentences without a confident label

Cites as background 4 papers
  • The theory of Birman and Hilden (developed over a series of papers in the 1970s, see the survey [ref] or [ref] ) relates $(S)$ to the mapping class group of the quotient $S / ι$.

    The Birman-Hilden theory · Hyperelliptic components and Birman–Hilden theory · 0.98

  • More recently, it has resurfaced in [ref] and [ref] and in a partial form in [ref] .]

    On the monodromy group of the family of smooth plane curves · Marked $r$–spin structures as winding numbers · 0.88

  • More recently, it has resurfaced in [ref] and [ref] and in a partial form in [ref] .]

    Monodromy and vanishing cycles in toric surfaces · Marked $r$–spin structures as winding numbers · 0.88

Discussion

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