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Given a simplicial complex with $n$ simplices, we consider the ConnectedSubsurface Recognition (c-SR) problem of finding a subcomplex that ishomeomorphic to a given connected surface with a fixed boundary. We also studythe related Sum-of-Genus Subsurface Recognition (SoG) problem, where we insteadsearch for a surface whose boundary, number of connected components, and totalgenus are given.  For both of these problems, we give parameterized algorithms with respect tothe treewidth $k$ of the Hasse diagram that run in $2^{O(k \log k)}n^{O(1)}$time. For the SoG problem, we also prove that our algorithm is optimal assumingthe exponential-time hypothesis. In fact, we prove the stronger result that ouralgorithm is ETH-tight even without restriction on the total genus.

ETH-tight algorithms for finding surfaces in simplicial complexes of bounded treewidth