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I think you are right about Mayer-Vietoris. It gives the isomorphism $H_n(sum)=H_n(M_1)\oplus H_n(M_2)$ and since homology classes can be represented by surfaces that don't hit "gluing disk" we get that the intersection form of the sum $Q=Q_1\oplus Q_2$.

If a manifold admits a smooth (or even PL) structure then KS vanishes.

In dimension 4:

I think that K-S invariant is independent of the intersection form if it is odd. If the form is odd then there're two homeomorphism types of manifolds (Freedman) that are distinguished by the $KS(M)\in H^4(M,\mathbb Z_2)$.

If the form is even then KS(M)=(1/8)signature mod 2.

If a manifold admits a smooth (or even PL) structure then KS vanishes.

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I think you are right about Mayer-Vietoris. It gives the isomorphism $H_n(sum)=H_n(M_1)\oplus H_n(M_2)$ and since homology classes can be represented by surfaces that don't hit "gluing disk" we get that the intersection form of the sum $Q=Q_1\oplus Q_2$.

I think that K-S invariant is independent of the intersection form if it is odd. If the form is odd then there're two homeomorphism types of manifolds (Freedman) that are distinguished by the $KS(M)\in H^4(M,\mathbb Z_2)$.

If the form is even then KS(M)=(1/8)signature mod 2.

If a manifold admits a smooth (or even PL) structure then KS vanishes.