[GAP Forum] 1-surgery on simplicial complex

[Marek Mitros]

Hi,

I am learning "simpcomp" package and I noticed function SCHandleAddition.
It performs 0-surgery on simplicial complex which is addition of the
handle. I wonder whether it is possible to develop function which will
perform 1-surgery along path in 1-skeleton of simplicial complex. Maybe it
is already implemented in other software used for 3-manifolds e.g. Regina.

Do you have any advice ?

My plan is to test 3-manifolds which are boundaries of 2-dimensional
CW-complex embedded in R^4. I observed that 2-complex with one word is
possible to embed in R^4. Therefore I will start with such two complexes.
My plan is following.
1. Represent bouquet of circles as connected sum S^1xS^2 #...# S^1xS^2.
Remember paths for generators of fundamental group.
2. For word w build path in 1-skeleton representing it.
3. Perform 1-surgery using function mentioned above.

Regards,
Marek