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If you really want to match only the dot, then StringComparison.Ordinal would be fastest, as there is no case-difference.
"Ordinal" doesn't use culture and/or casing rules that are not applicable anyway on a symbol like a ..
You seem to be doing file name comparisons, so I would just add that OrdinalIgnoreCase is closest to what NTFS does (it's not exactly the same, but it's closer than InvariantCultureIgnoreCase)