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 $\#^kS^1\times B^3$...
Asked
Active
Viewed 88 times
0
-
I means connected sum. – bsbb4 Mar 10 '21 at 09:56
-
Connected sum – user10354138 Mar 10 '21 at 09:56
2 Answers
0
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:
Dietrich Burde
- 130,978
-
Not quite: In this particular case, Kirby means the "boundary connected sum" which is not the same as the ordinary connected sum. – Moishe Kohan Mar 10 '21 at 12:24
-
@MoisheKohan I see, thank you. Still, for the OP it is good to know the symbol in general first. Further details depend of course on the context. – Dietrich Burde Mar 10 '21 at 12:28
0
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.
Moishe Kohan
- 97,719