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math.GT2025
The Lodha--Moore groups and their -adic generalizations are not SCY
Yuya Kodama, Akihiro Takano
A closed 4-manifold is symplectic Calabi--Yau (SCY) if its canonical class is trivial. Friedl and Vidussi proved that Thompson's group cannot be the fundamental group of any SC…
math.GT2024
The Long--Moody construction and twisted Alexander invariants
Akihiro Takano
In 1994, Long and Moody introduced a method to construct a new representation of the braid group from the representation of the braid group or the semidirect product of the braid g…