Homology of connected sum

This article describes the effect of the connected sum operation on the following invariant: homology groups

Statement

Suppose $M_{1}$ and $M_{2}$ are the connected manifolds of dimension $n$ whose connected sum is being taken. Assume both We have:

Case for $p$	Additional condition on $M_{1},M_{2}$	What is known about $H_{p}(M_{1})$ and $H_{p}(M_{2})$?	Formula for $H_{p}(M_{1}\#M_{2})$ in terms of homology groups of $M_{1}$ and $M_{2}$
0	none	both isomorphic to $\mathbb {Z}$	$\mathbb {Z}$ (because both are connected, so is their connected sum).
Greater than 0, less than $n-1$	none	both are finitely generated abelian groups	$H_{p}(M_{1})\oplus H_{p}(M_{2})$
$n-1$	Both manifolds are compact, at least one of them is orientable	both are finitely generated abelian groups, at least one is free abelian	$H_{n-1}(M_{1})\oplus H_{n-1}(M_{2})$
$n-1$	other cases	?	?
$n$	Both are compact and orientable	both are $\mathbb {Z}$	$\mathbb {Z}$
$n$	other cases	?	?
Greater than $n$	none	both are zero groups	0

Euler characteristic

The Euler characteristics are related by the following formula when both $M_{1}$ and $M_{2}$ are compact connected manifolds:

$\chi (M_{1}\#M_{2})=\chi (M_{1})+\chi (M_{2})-\chi (S^{n})$