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math.GT2025
Homotopy Type of the Space of Fibrations of the Three-sphere by Simple Closed Curves
Dennis Deturck, Ziqi Fang, Herman Gluck +4
We show that the moduli space of all smooth fibrations of a three-sphere by simple closed curves has the homotopy type of a disjoint union of a pair of two-spheres if the fibers ar…
math.AT2025
Parametrized scissors congruence -theory of manifolds and cobordism categories
Mona Merling, George Raptis, Julia Semikina
We introduce a parametrized version of scissors congruence -theory of manifolds with tangential structure, which includes a topologized version of the scissors congruence -th…
math.AT2025
Scissors congruence K-theory for equivariant manifolds
Mona Merling, Ming Ng, Julia Semikina +2
We introduce a scissors congruence -theory spectrum which lifts the equivariant scissors congruence groups for compact -manifolds with boundary, and we show that on thi…