What does "#" mean here? "[these structures] are diffeomorphic to $\#^kS^1\times B^3$"

Question

I am reading The topology of 4-manifolds by Kirby.

At page 7 the author uses the symbol # what does it mean?

The sentence for context is this:

However, the 3-handles and 4-handle of a closed $M^4$ together are diffeomorphic to $\#^kS^1\times B^3$...

Answer 1

It means connected sum, e.g. $S^1 \# S^1$. For details see, for example,

connected sum of surfaces is well defined proof attempt

For the "iterated" notation see here:

notation for connected sum $\#^n S^2 \times S^2$

Answer 2

In this particular passage, notation $\#$ is for the boundary connected sum, see my answer here for the detailed definition and comparison to the usual connected sum.

Incidentally, one should be very proficient in basic algebraic topology to have any chance succeeding in reading Kirby's book.