The moduli space of Type~A surfaces with torsion and non-singular symmetric Ricci tensor

Abstract

We examine the moduli spaces of Type A connections on oriented and unoriented surfaces both with and without torsion in relation to the signature of the associated symmetric Ricci tensor ρs. If the signature of ρs is (1, 1) or (0, 2), the spaces are smooth. If the signature is (2, 0), there is an orbifold singularity.2010 Mathematics Subject Classification. 53C21.

Moduli spaces of type $$\mathcal {B}$$ B surfaces with torsion

“…The action is said to be fixed point free if G P = {id} for all P . The action is said to be proper if given points P n ∈ N and g n ∈ G with P n → P ∈ N and g n P n → P ∈ N , we can choose a convergent subsequence so g n k → g ∈ G. We refer to [5,27] for the proof of the following result; see also the discussion in [28].…”

“…As the Type A setting was discussed in [6,7,28], we shall concentrate on the Type B setting in this paper. We introduce some notational conventions:…”

Moduli spaces of oriented Type A manifolds of dimension at least 3

“…The remainder of this paper is devoted to the study of these geometries. Since case of surfaces is dealt with in [7,8,30], we shall assume for the remainder of this paper that m = p + q ≥ 3; there are phenomena in this setting not found in the case m = 2.…”

“…The action is said to be fixed point free if G P = {id} for all P . The action is said to be proper if given points P n ∈ N and g n ∈ G with P n → P ∈ N and g n P n → P ∈ N , we can choose a convergent subsequence so g n k → g ∈ G. We refer to [6,29] for the proof of the following result; see also the discussion in [30].…”