8 papers
Topological symmetric and braid homologies
Gabriel Angelini-Knoll, David Chan, Teena Gerhardt +2
We identify topological symmetric homology as the free -algebra on an -algebra and topological braid homology as the free -algebra on…
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…
Topological homology of rings with twisted -action
Gabriel Angelini-Knoll, Mona Merling, Maximilien Péroux
We construct topological -homology for rings with twisted -action. Here a ring with twisted -action is a common generalization of a ring with anti-involution and a ring…
Algebraic -theory for squares categories
Jonathan Campbell, Josefien Kuijper, Mona Merling +1
In this paper we introduce a new formalism for -theory, called squares -theory. This formalism allows us to simultaneously generalize the usual three-term relation $[B] = [A]…
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 th…
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…