The Witten–Reshetikhin–Turaev invariant for links in finite order mapping tori I

Jørgen Ellegaard Andersen; Benjamin Himpel; Søren Fuglede Jørgensen; Johan Martens; Brendan Donald Kenneth McLellan

doi:10.1016/j.aim.2016.08.042

The Witten–Reshetikhin–Turaev invariant for links in finite order mapping tori I

Jørgen Ellegaard Andersen, Benjamin Himpel, Søren Fuglede Jørgensen, Johan Martens, Brendan Donald Kenneth McLellan

Aarhus University

Research output: Contribution to journal › Journal article › Research › peer-review

Abstract

We state Asymptotic Expansion and Growth Rate conjectures for the Witten–Reshetikhin–Turaev invariants of arbitrary framed links in 3-manifolds, and we prove these conjectures for the natural links in mapping tori of finite-order automorphisms of marked surfaces. Our approach is based upon geometric quantisation of the moduli space of parabolic bundles on the surface, which we show coincides with the construction of the Witten–Reshetikhin–Turaev invariants.

Original language	English
Journal	Advances in Mathematics
Volume	304
Pages (from-to)	131-178
ISSN	0001-8708
DOIs	https://doi.org/10.1016/j.aim.2016.08.042
Publication status	Published - 2. Jan 2017
Externally published	Yes

Keywords

Asymptotic expansion conjecture
Chern–Simons theory
Gauge theory
Growth rate conjecture
TQFT
Witten–Reshetikhin–Turaev link invariants

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10.1016/j.aim.2016.08.042

Cite this

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title = "The Witten–Reshetikhin–Turaev invariant for links in finite order mapping tori I",

abstract = "We state Asymptotic Expansion and Growth Rate conjectures for the Witten–Reshetikhin–Turaev invariants of arbitrary framed links in 3-manifolds, and we prove these conjectures for the natural links in mapping tori of finite-order automorphisms of marked surfaces. Our approach is based upon geometric quantisation of the moduli space of parabolic bundles on the surface, which we show coincides with the construction of the Witten–Reshetikhin–Turaev invariants.",

keywords = "Asymptotic expansion conjecture, Chern–Simons theory, Gauge theory, Growth rate conjecture, TQFT, Witten–Reshetikhin–Turaev link invariants",

author = "Andersen, {J{\o}rgen Ellegaard} and Benjamin Himpel and J{\o}rgensen, {S{\o}ren Fuglede} and Johan Martens and McLellan, {Brendan Donald Kenneth}",

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doi = "10.1016/j.aim.2016.08.042",

language = "English",

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journal = "Advances in Mathematics",

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TY - JOUR

T1 - The Witten–Reshetikhin–Turaev invariant for links in finite order mapping tori I

AU - Andersen, Jørgen Ellegaard

AU - Himpel, Benjamin

AU - Jørgensen, Søren Fuglede

AU - Martens, Johan

AU - McLellan, Brendan Donald Kenneth

PY - 2017/1/2

Y1 - 2017/1/2

N2 - We state Asymptotic Expansion and Growth Rate conjectures for the Witten–Reshetikhin–Turaev invariants of arbitrary framed links in 3-manifolds, and we prove these conjectures for the natural links in mapping tori of finite-order automorphisms of marked surfaces. Our approach is based upon geometric quantisation of the moduli space of parabolic bundles on the surface, which we show coincides with the construction of the Witten–Reshetikhin–Turaev invariants.

AB - We state Asymptotic Expansion and Growth Rate conjectures for the Witten–Reshetikhin–Turaev invariants of arbitrary framed links in 3-manifolds, and we prove these conjectures for the natural links in mapping tori of finite-order automorphisms of marked surfaces. Our approach is based upon geometric quantisation of the moduli space of parabolic bundles on the surface, which we show coincides with the construction of the Witten–Reshetikhin–Turaev invariants.

KW - Asymptotic expansion conjecture

KW - Chern–Simons theory

KW - Gauge theory

KW - Growth rate conjecture

KW - TQFT

KW - Witten–Reshetikhin–Turaev link invariants

U2 - 10.1016/j.aim.2016.08.042

DO - 10.1016/j.aim.2016.08.042

M3 - Journal article

SN - 0001-8708

VL - 304

SP - 131

EP - 178

JO - Advances in Mathematics

JF - Advances in Mathematics

ER -

The Witten–Reshetikhin–Turaev invariant for links in finite order mapping tori I

Abstract

Keywords

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