Complex sentence: High-dimensional topology means manifolds of dimension 5 and above, or in relative terms, embeddings in codimension 3 and above, while low-dimensional topology, concerning questions of dimensions up to 4, or embeddings in codimension up to 2.
Split into simpler sentences: High-dimensional topology refers to manifolds of dimension 5 and above, or in relative terms, embeddings in codimension 3 and above. Low-dimensional topology is concerned with questions in dimensions up to 4, or embeddings in codimension up to 2.