Splitting the mapping class group extension for connected sums of equal-dimensional sphere products

Determine whether the exact sequence relating the Torelli group, the mapping class group, and the group G_g splits for the connected sum of g copies of S^p × S^p when g = 1 and p = 7.

Background

The paper compares its mapping class group calculations for connected sums of S^p × S^{p+1} with known results for connected sums of S^p × S^p. For odd p, prior work establishes nonsplitting for g ≥ 2 and splitting for g = 1 except when p = 3 or 7. The remaining case g = 1, p = 7 is explicitly identified as unresolved.