A fact that one can find in many books is that the monodromy of a Lefschetz fibration is the product of right-handed/positive Dehn twists (one for each vanishing cycle).
The only proof I could find for that is this book by Gompf and Stipsicz. I'm looking for a proof that does not use Kirby diagrams. Can anybody help me out with books or papers that proof this fact in a different way?
Thanks for any help or references!
Check out a paper by Paul Seidel called something like “a long exact sequence for Floer cohomology groups “(around 2000) In there early in the paper in thesection “Dehn twists and all that” you will see a calculation of the monochromy for Pi : C^n to C with Pi = sum zj^2. The non singular fibre of Pi is T^*S^n-1 and this is the local model for a vanishing cycle S^n-1. He shows the monodromy is a generalized Dehn twist about S^n-1. For four manifolds the local model will be T^*S^1 and it will be a usual Dehn twist. This generalized Dehn twist observation is originally due to Arnold so he probably has a paper about it as well in the 80s or 90s which might be an nicer read.