Remarks on Congruence of 3-manifolds

We give two proofs that the 3-torus is not weakly d-congruent to the connected sum of three S^1xS^2’s, if d>2. We study how cohomology ring structure relates to weak congruence. We give an example of three 3–manifolds which are weakly 5-congruent but are not 5-congruent.