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math.GT2022
Crossing numbers and rotation numbers of cycles in a plane immersed graph
Ayumu Inoue, Naoki Kimura, Ryo Nikkuni +1
For any generic immersion of a Petersen graph into a plane, the number of crossing points between two edges of distance one is odd. The sum of the crossing numbers of all -cycle…
math.GT2018
A generalization of the Dijkgraaf-Witten invariants for cusped 3-manifolds
Naoki Kimura
We introduce a generalization of the Dijkgraaf-Witten invariants for cusped or compact oriented 3-manifolds. We show that the generalized DW invariants distinguish some pairs of cu…