Conditions of smoothness of moduli spaces of flat connections and of character varieties

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Conditions of smoothness of moduli spaces of flat connections and of character varieties. / Ho, Nankuo; Wilkin, Graeme Peter Desmond; Wu, Siye.

In: Mathematische Zeitschrift, 14.11.2018.

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Ho, N, Wilkin, GPD & Wu, S 2018, 'Conditions of smoothness of moduli spaces of flat connections and of character varieties', Mathematische Zeitschrift. https://doi.org/10.1007/s00209-018-2158-2

APA

Ho, N., Wilkin, G. P. D., & Wu, S. (2018). Conditions of smoothness of moduli spaces of flat connections and of character varieties. Mathematische Zeitschrift. https://doi.org/10.1007/s00209-018-2158-2

Vancouver

Ho N, Wilkin GPD, Wu S. Conditions of smoothness of moduli spaces of flat connections and of character varieties. Mathematische Zeitschrift. 2018 Nov 14. https://doi.org/10.1007/s00209-018-2158-2

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Ho, Nankuo ; Wilkin, Graeme Peter Desmond ; Wu, Siye. / Conditions of smoothness of moduli spaces of flat connections and of character varieties. In: Mathematische Zeitschrift. 2018.

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@article{61691baa370c42bcb077058b703f5c0f,
title = "Conditions of smoothness of moduli spaces of flat connections and of character varieties",
abstract = "We use gauge theoretic and algebraic methods to examine sufficient conditions for smooth points on the moduli space of flat connections on a compact manifold and on the character variety of a finitely generated and presented group. We give a complete proof of the slice theorem for the action of the group of gauge transformations on the space of flat connections. Consequently, the slice is smooth if the second cohomology of the manifold with coefficients in the semisimple part of the adjoint bundle vanishes. On the other hand, we find that the smoothness of the slice for the character variety of a finitely generated and presented group depends not only on the second group cohomology but also on the relation module of the presentation. However, when there is a single relator or if there is no relation among the relators in the presentation, our condition reduces to the minimality of the second group cohomology. This is also verified using Fox calculus. Finally, we compare the conditions of smoothness in the two approaches.",
author = "Nankuo Ho and Wilkin, {Graeme Peter Desmond} and Siye Wu",
note = "{\circledC} Springer-Verlag GmbH Germany, part of Springer Nature 2018. This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details.",
year = "2018",
month = "11",
day = "14",
doi = "10.1007/s00209-018-2158-2",
language = "English",
journal = "Mathematische Zeitschrift",
issn = "0025-5874",
publisher = "Springer New York",

}

RIS (suitable for import to EndNote) - Download

TY - JOUR

T1 - Conditions of smoothness of moduli spaces of flat connections and of character varieties

AU - Ho, Nankuo

AU - Wilkin, Graeme Peter Desmond

AU - Wu, Siye

N1 - © Springer-Verlag GmbH Germany, part of Springer Nature 2018. This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details.

PY - 2018/11/14

Y1 - 2018/11/14

N2 - We use gauge theoretic and algebraic methods to examine sufficient conditions for smooth points on the moduli space of flat connections on a compact manifold and on the character variety of a finitely generated and presented group. We give a complete proof of the slice theorem for the action of the group of gauge transformations on the space of flat connections. Consequently, the slice is smooth if the second cohomology of the manifold with coefficients in the semisimple part of the adjoint bundle vanishes. On the other hand, we find that the smoothness of the slice for the character variety of a finitely generated and presented group depends not only on the second group cohomology but also on the relation module of the presentation. However, when there is a single relator or if there is no relation among the relators in the presentation, our condition reduces to the minimality of the second group cohomology. This is also verified using Fox calculus. Finally, we compare the conditions of smoothness in the two approaches.

AB - We use gauge theoretic and algebraic methods to examine sufficient conditions for smooth points on the moduli space of flat connections on a compact manifold and on the character variety of a finitely generated and presented group. We give a complete proof of the slice theorem for the action of the group of gauge transformations on the space of flat connections. Consequently, the slice is smooth if the second cohomology of the manifold with coefficients in the semisimple part of the adjoint bundle vanishes. On the other hand, we find that the smoothness of the slice for the character variety of a finitely generated and presented group depends not only on the second group cohomology but also on the relation module of the presentation. However, when there is a single relator or if there is no relation among the relators in the presentation, our condition reduces to the minimality of the second group cohomology. This is also verified using Fox calculus. Finally, we compare the conditions of smoothness in the two approaches.

U2 - 10.1007/s00209-018-2158-2

DO - 10.1007/s00209-018-2158-2

M3 - Article

JO - Mathematische Zeitschrift

JF - Mathematische Zeitschrift

SN - 0025-5874

ER -