In a book I read:
$M$ and $N$ are $d$-dimensional manifolds. Let $\widetilde{M}$ be the $(d−1)$-skeleton of $M$, or equivalently, $\widetilde{M}$ is obtained from $M$ by removing a disc in the interior of the $d$-cell of $M$. Define $\widetilde{N}$ similarly. Suppose that $f: S^{d−1} \to \widetilde{M}$ and $g: S^{d−1} \to \widetilde{N}$ are the attaching maps for the top cells in $M$ and $N$. Then the attaching map for the top cell in the connected sum $M\#N$ is $S^{d−1}\xrightarrow{f+g} \widetilde{M}\vee\widetilde{N}$.
So far, the denotation $f+g$ looks like just a denotation, however later the book deals with a specific example of manifold $S^3\times S^4$, where the attaching map $S^6 \to S^3 \vee S^4$ for its top cell is the Whitehead product $[s_1, s_2]_w$, where $s_1$ and $s_2$ respectively are the inclusions of $S^3$ and $S^4$ into $S^3 \vee S^4$. The attaching map for the top cell of the connected sum $(S^3 \times S^4)\#(S^3 \times S^4)$ is therefore the sum of two such Whitehead products. Finally, it is said that passing to the adjoint map we obtain $[a_1,b_2]+[a_2,b_2]$ for $a_i,b_i\in H_*(\Omega X).$
There are specific $a_i,b_i$ offered in the book, but I don't think it is very relevant to the question.
So, my question is: where does the denotation $f+g$ come from? Does this map has some kind of a property of transforming into a real sum when passing to adjoint maps?