In his Ph. D. thesis, Burak Ozbagci described an algorithm computing signatures of Lefschetz fibrations where the input is a factorization of the monodromy into a product of Dehn twists. I will talk about a reformulation of Ozbagci's algorithm which becomes much easier to implement. Our main tool will be Wall's non-additivity formula applied to what I call partial fiber sum decomposition of a Lefschetz fibrations over disk. This is a joint work with A. Cengel.
Links:
[1] https://www.mpim-bonn.mpg.de/de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/de/node/3444
[3] https://www.mpim-bonn.mpg.de/de/TopologySeminar