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Basic Kirwan Surjectivity for K-Contact Manifolds

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Lana Casselmann

Differential Geometry · Submitted 14 Oct 2016

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

The authors' main claim We prove an analogue of Kirwan surjectivity in the setting of equivariant basic cohomology of K-contact manifolds.

how it is stated · asserted 1.00 read the record →

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arXiv ID1610.04374 (version 2)
Pith ID2JGXBUD7, Pith's permanent record of this paper and its review
CitationLana Casselmann. "Basic Kirwan Surjectivity for K-Contact Manifolds." arXiv:1610.04374 (2016). https://pith.science/paper/2JGXBUD7
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,104 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.29 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.93 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

We prove an analogue of Kirwan surjectivity in the setting of equivariant basic cohomology of K-contact manifolds. If the Reeb vector field induces a free $S^1$-action, the $S^1$-quotient is a symplectic manifold and our result reproduces Kirwan's surjectivity for these symplectic manifolds. We further prove a Tolman-Weitsman type description of the kernel of the basic Kirwan map for $S^1$-actions and show that torus actions on a K-contact manifold that preserve the contact form and admit 0 as a regular value of the contact moment map are equivariantly formal in the basic setting.

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 We prove an analogue of Kirwan surjectivity in the setting of equivariant basic cohomology of K-contact manifolds. contribution 0.59 0.97 0.93 asserted 1.00
s1 If the Reeb vector field induces a free $S^1$-action, the $S^1$-quotient is a symplectic manifold and our result reproduces Kirwan's surjectivity for these symplectic manifolds. interpretation 0.79 0.74 0.14 asserted 1.00
s2 We further prove a Tolman-Weitsman type description of the kernel of the basic Kirwan map for $S^1$-actions and show that torus actions on a K-contact manifold that preserve the contact form and admit 0 as a regular value of the contact moment map are equivariantly formal in the basic setting. result 0.65 0.95 0.15 asserted 1.00

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

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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

We prove an analogue of Kirwan surjectivity in the setting of equivariant basic cohomology of K-contact manifolds. If the Reeb vector field induces a free $S^1$-action, the $S^1$-quotient is a symplectic manifold and our result reproduces Kirwan's surjectivity for these symplectic manifolds. We further prove a Tolman-Weitsman type description of the kernel of the basic Kirwan map for $S^1$-actions and show that torus actions on a K-contact manifold that preserve the contact form and admit 0 as a regular value of the contact moment map are equivariantly formal in the basic setting.

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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 · 5 sentences without a confident label

Builds on 2 papers
  • The proof of [ref] is equally applicable in the basic (see also [ref] ) and boundary setting so that we obtain Let $(N,A,ℰ)$ be as in Definition [ref].

    Localization for $K$-Contact Manifolds · Equivariant basic Cohomology · 0.95

  • The considerations of [ref] carry over to the basic setting so that we also obtain an excision statement for open submanifolds.

    Equivariant relative Thom forms and Chern characters · Equivariant basic Cohomology · 0.98

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