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Multisymplectic Structures and Higher Momentum Maps

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Nestor Leon Delgado

Symplectic Geometry · Submitted 4 Nov 2018

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

The authors' main claim Lastly, the third one establishes the equivalence between cochain-homotopies to Q(D) and L-infinity algebra lifts satisfying certain properties.

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arXiv ID1811.01415 (version 2)
Pith IDL7VVSYKI, Pith's permanent record of this paper and its review
CitationNestor Leon Delgado. "Multisymplectic Structures and Higher Momentum Maps." arXiv:1811.01415 (2018). https://pith.science/paper/L7VVSYKI
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 6,146 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.08 · human participants 0.02 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.23 · compares with prior results 0.07 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

This document is a reorganization of the results on the Master Thesis of the same title written by the author under the supervision of Dr. Christian Blohmann at the University of Bonn in 2014. There are three main results in this document. The first one is a construction of a high L-infinity algebra out of any Gerstenhaber algebra. The second one uses a cochain null-homotopy from the Chevalley-Eilenberg complex associated to a graded Lie algebra to any cochain complex D to induce (transfer) the L-infinity algebra structure from the Lie alegebra to Q(D), a resolution of D. Lastly, the third one establishes the equivalence between cochain-homotopies to Q(D) and L-infinity algebra lifts satisfying certain properties. All the three results are motivated from the study of multi-symplectic structures. In particular, the definition of comomentum maps in multi-symplectic manifolds.

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 document is a reorganization of the results on the Master Thesis of the same title written by the author under the supervision of Dr. background 0.99 0.24 0.02 asserted 0.98
s1 Christian Blohmann at the University of Bonn in 2014. background 1.00 0.12 0.01 asserted 0.89
s2 There are three main results in this document. contribution 0.81 0.36 0.05 asserted 1.00
s3 The first one is a construction of a high L-infinity algebra out of any Gerstenhaber algebra. result 0.84 0.87 0.21 asserted 1.00
s4 The second one uses a cochain null-homotopy from the Chevalley-Eilenberg complex associated to a graded Lie algebra to any cochain complex D to induce (transfer) the L-infinity algebra structure from the Lie alegebra to Q(D), a resolution of D. result 0.73 0.83 0.13 asserted 1.00
s5 Lastly, the third one establishes the equivalence between cochain-homotopies to Q(D) and L-infinity algebra lifts satisfying certain properties. result 0.98 0.90 0.24 asserted 1.00
s6 All the three results are motivated from the study of multi-symplectic structures. background 0.74 0.35 0.09 asserted 1.00
s7 In particular, the definition of comomentum maps in multi-symplectic manifolds. background 0.80 0.21 0.06 unclear 0.74

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

This document is a reorganization of the results on the Master Thesis of the same title written by the author under the supervision of Dr. Christian Blohmann at the University of Bonn in 2014. There are three main results in this document. The first one is a construction of a high L-infinity algebra out of any Gerstenhaber algebra. The second one uses a cochain null-homotopy from the Chevalley-Eilenberg complex associated to a graded Lie algebra to any cochain complex D to induce (transfer) the L-infinity algebra structure from the Lie alegebra to Q(D), a resolution of D. Lastly, the third one establishes the equivalence between cochain-homotopies to Q(D) and L-infinity algebra lifts satisfying certain properties. All the three results are motivated from the study of multi-symplectic structures. In particular, the definition of comomentum maps in multi-symplectic manifolds.

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