A McShane identity for once-punctured super tori
Classical Teichmueller theory is the study of marked hyperbolic surfaces, and Penner's decorated Teichmueller theory is a particular algebraic approach which has resulted in powerful and wide-reaching generalizations via Fock and Goncharov's version of higher Teichmueller theory. There has been exciting recent progress in a different direction: super decorated Teichmueller theory, whereby the role traditionally taken up by the real numbers R is supplanted by a non-commutative Grassmann algebra. This generalised theory corresponds to super hyperbolic surfaces, and we establish McShane identities for once-punctured super tori. We also study the asymptotic behaviour of the super length spectrum for the set of simple closed geodesics for once-punctured super tori.
Dr Yi Huang, Yau Mathematical Science Center, Tsinghua University