Research output: Working paper › Research

**Asymptotic aspects of the Teichmüller TQFT.** / Andersen, Jørgen Ellegaard; Nissen, Jens-Jakob Kratmann.

Research output: Working paper › Research

Andersen, JE & Nissen, J-JK 2016 'Asymptotic aspects of the Teichmüller TQFT' arXiv.org.

Andersen, J. E., & Nissen, J-J. K. (2016). *Asymptotic aspects of the Teichmüller TQFT*. arXiv.org.

Andersen JE, Nissen J-JK. 2016. Asymptotic aspects of the Teichmüller TQFT. arXiv.org.

Andersen, Jørgen Ellegaard and Jens-Jakob Kratmann Nissen *Asymptotic aspects of the Teichmüller TQFT*. arXiv.org. 2016., 55 p.

Andersen JE, Nissen J-JK. Asymptotic aspects of the Teichmüller TQFT. arXiv.org. 2016 Dec 21.

Andersen, Jørgen Ellegaard ; Nissen, Jens-Jakob Kratmann. / **Asymptotic aspects of the Teichmüller TQFT**. arXiv.org, 2016.

@techreport{5e096ca100e3413b89dd616c1293b13c,

title = "Asymptotic aspects of the Teichm{\"u}ller TQFT",

abstract = "We calculate the knot invariant coming from the Teichm{\"u}ller TQFT [AK1]. Specifically we calculate the knot invariant for the complement of the knot 61 both in the original [AK1] and the new formulation of the Teichm{\"u}ller TQFT [AK2] for the one-vertex H-triangulation of (S 3, 61).We show that the two formulations give equivalent answers. Furthermore we apply a formal stationary phase analysis and arrive at the AndersenKashaevvolume conjecture as stated in [AK1, Conj. 1].Furthermore we calculate the first examples of knot complements in the new formulation showing that the new formulation is equivalent to the original one in all the special cases considered.Finally, we provide an explicit isomorphism between the Teichm{\"u}ller TQFT representation of the mapping class group of a once punctured torus and a representation of this mapping class group on the space of Schwartz class functions on the real line.",

author = "Andersen, {J{\o}rgen Ellegaard} and Nissen, {Jens-Jakob Kratmann}",

year = "2016",

month = "12",

day = "21",

language = "English",

publisher = "arXiv.org",

type = "WorkingPaper",

institution = "arXiv.org",

}

TY - UNPB

T1 - Asymptotic aspects of the Teichmüller TQFT

AU - Andersen, Jørgen Ellegaard

AU - Nissen, Jens-Jakob Kratmann

PY - 2016/12/21

Y1 - 2016/12/21

N2 - We calculate the knot invariant coming from the Teichmüller TQFT [AK1]. Specifically we calculate the knot invariant for the complement of the knot 61 both in the original [AK1] and the new formulation of the Teichmüller TQFT [AK2] for the one-vertex H-triangulation of (S 3, 61).We show that the two formulations give equivalent answers. Furthermore we apply a formal stationary phase analysis and arrive at the AndersenKashaevvolume conjecture as stated in [AK1, Conj. 1].Furthermore we calculate the first examples of knot complements in the new formulation showing that the new formulation is equivalent to the original one in all the special cases considered.Finally, we provide an explicit isomorphism between the Teichmüller TQFT representation of the mapping class group of a once punctured torus and a representation of this mapping class group on the space of Schwartz class functions on the real line.

AB - We calculate the knot invariant coming from the Teichmüller TQFT [AK1]. Specifically we calculate the knot invariant for the complement of the knot 61 both in the original [AK1] and the new formulation of the Teichmüller TQFT [AK2] for the one-vertex H-triangulation of (S 3, 61).We show that the two formulations give equivalent answers. Furthermore we apply a formal stationary phase analysis and arrive at the AndersenKashaevvolume conjecture as stated in [AK1, Conj. 1].Furthermore we calculate the first examples of knot complements in the new formulation showing that the new formulation is equivalent to the original one in all the special cases considered.Finally, we provide an explicit isomorphism between the Teichmüller TQFT representation of the mapping class group of a once punctured torus and a representation of this mapping class group on the space of Schwartz class functions on the real line.

M3 - Working paper

BT - Asymptotic aspects of the Teichmüller TQFT

PB - arXiv.org

ER -