10 papers
A genuine -spectrum for the cut-and-paste -theory of -manifolds
Maxine Calle, David Chan
Recent work has applied scissors congruence -theory to study classical cut-and-paste () invariants of manifolds. This paper proves the conjecture that the squares -theory…
On the classifying space of a Morse flow category
Maxine E. Calle, Fangji Liu
We show that the classifying space of the flow category of a \emph{tame} Morse function on a smooth, closed manifold recovers the homotopy type of , thereby addressing a cla…
Squares K-theory and 2-Segal spaces
Maxine E. Calle, Maru Sarazola
We define an -construction for squares categories, and introduce a class of squares categories we call "proto-Waldhausen" which capture the properties required for the $…
Segal K-theory factors through Waldhausen categories
Maxine E. Calle, David Chan
We show that Segal's K-theory of symmetric monoidal categorizes can be factored through Waldhausen categories. In particular, given a symmetric monoidal category , we produce a…
Equivariant Trees and Partition Complexes
Julia E. Bergner, Peter Bonventre, Maxine E. Calle +2
We introduce two definitions of -equivariant partitions of a finite -set, both of which yield -equivariant partition complexes. By considering suitable notions of equivari…
A linearization map for genuine equivariant algebraic -theory
Maxine Calle, David Chan, Andres Mejia
We introduce a version of algebraic -theory for coefficient systems of rings which is valued in genuine -spectra for a finite group . We use this construction to build a g…