10 citations · 43 across the 24 of their papers we have counts for
31 papers
The Becker--Gottlieb transfer is not functorial: An example based on units of group rings
Georg Lehner, Cary Malkiewich, Florian Naef
We show by explicit counterexample that the Becker--Gottlieb transfer cannot be made functorial. A different counterexample using rational homotopy theory was discovered concurrent…
Scissors automorphism groups II: Solomon-Tits theorems
Alexander Kupers, Ezekiel Lemann, Cary Malkiewich +2
The Solomon-Tits theorem says that the poset of proper non-trivial subspaces of a finite-dimensional vector space has realisation equivalent to a wedge of spheres. In this paper we…
Higher Spherical Scissors Congruence I: Hopf Algebra
Inbar Klang, Josefien Kuijper, Cary Malkiewich +2
In the study of the generalization of Hilbert's Third Problem to spherical geometry, Sah constructed a Hopf algebra of spherical polytopes with product given by join and coproduct…
From Hopf Algebras in Model Categories to Hopf Algebras in -categories
Inbar Klang, Josefien Kuijper, Cary Malkiewich +2
We show that algebra objects in model categories can be transferred to algebra objects in -categories, without any cofibrancy or fibrancy assumptions on the algebra. We fur…
Scissors automorphism groups I: Homological stability and K-theory
Alexander Kupers, Ezekiel Lemann, Cary Malkiewich +2
In any category with a reasonable notion of cover, each object has a group of scissors automorphisms. We prove that under mild conditions, the homology of this group is independent…
A concise proof of the stable model structure on symmetric spectra
Cary Malkiewich, Maru Sarazola
It is well-known that the stable model structure on symmetric spectra cannot be transferred from the one on sequential spectra through the forgetful functor. We use the fibrant tra…
Smash powers and traces on parametrized spectra: An application of rigidity
Cary Malkiewich, Kate Ponto
The bicategory of parametrized spectra has a remarkably rich structure. We can take traces in this bicategory, giving classical invariants that count fixed points. We can also take…
A convenient category of parametrized spectra
Cary Malkiewich
We describe a point-set category of parametrized orthogonal spectra, a model structure on this category, and a separate, more geometric class of cofibrant-and-fibrant objects. The…
On the functoriality of the space of equivariant smooth -cobordisms
Thomas Goodwillie, Kiyoshi Igusa, Cary Malkiewich +1
We construct an -functor that takes each smooth -manifold with corners to the space of equivariant smooth -cobordisms . We al…
A trace map on higher scissors congruence groups
Anna Marie Bohmann, Teena Gerhardt, Cary Malkiewich +2
Cut-and-paste -theory has recently emerged as an important variant of higher algebraic -theory. However, many of the powerful tools used to study classical higher algebraic $…
On the multiplicativity of the Euler characteristic
John R. Klein, Cary Malkiewich, Maxime Ramzi
In this short paper, we give two proofs that the Euler characteristic is multiplicative, for fiber sequences of finitely dominated spaces. This is equivalent to proving that the Be…
On higher scissors congruence
Cary Malkiewich
We solve the higher version of Hilbert's Third Problem for one-dimensional geometries, and in higher dimensions we reduce the problem to a computation in group homology. Our centra…
Coherence for bicategories, lax functors, and shadows
Cary Malkiewich, Kate Ponto
Coherence theorems are fundamental to how we think about monoidal categories and their generalizations. In this paper we revisit Mac Lane's original proof of coherence for monoidal…
-theoretic torsion and the zeta function
John R. Klein, Cary Malkiewich
We generalize to higher algebraic -theory an identity (originally due to Milnor) that relates the Reidemeister torsion of an infinite cyclic cover to its Lefschetz zeta function…
-theory of endomorphisms, the -trace, and zeta functions
Jonathan A. Campbell, John A. Lind, Cary Malkiewich +2
We show that the characteristic polynomial and the Lefschetz zeta function are manifestations of the trace map from the -theory of endomorphisms to topological restriction homol…
Spectral Waldhausen categories, the -construction, and the Dennis trace
Jonathan A. Campbell, John A. Lind, Cary Malkiewich +2
We give an explicit point-set construction of the Dennis trace map from the -theory of endomorphisms to topological Hochschild homology $\mathrm{THH…
The equivariant parametrized -cobordism theorem, the non-manifold part
Cary Malkiewich, Mona Merling
We construct a map from the suspension -spectrum of a smooth compact -manifold to the equivariant -theory spectrum , and we show that its fiber is,…
Parametrized spectra, a low-tech approach
Cary Malkiewich
We give an alternative treatment of the foundations of parametrized spectra, with an eye toward applications in fixed-point theory. We cover most of the central results from the bo…
Coassembly is a homotopy limit map
Cary Malkiewich, Mona Merling
We prove a claim by Williams that the coassembly map is a homotopy limit map. As an application, we show that the homotopy limit map for the coarse version of equivariant -theor…
Coherence for indexed symmetric monoidal categories
Cary Malkiewich, Kate Ponto
Indexed symmetric monoidal categories are an important refinement of bicategories -- this structure underlies several familiar bicategories, including the homotopy bicategory of pa…
Periodic points and topological restriction homology
Cary Malkiewich, Kate Ponto
We answer in the affirmative two conjectures made by Klein and Williams. First, in a range of dimensions, the equivariant Reidemeister trace defines a complete obstruction to remov…
The user's guide project: giving experiential context to research papers
Cary Malkiewich, Mona Merling, David White +2
This paper was written in 2015, and published in the Journal of Humanistic Mathematics. This paper announces the first issue (2015) of Enchiridion: Mathematics User's Guides, a pro…
Comparing cyclotomic structures on different models for topological Hochschild homology
Emanuele Dotto, Cary Malkiewich, Irakli Patchkoria +2
The topological Hochschild homology of an orthogonal ring spectrum can be defined by evaluating the cyclic bar construction on or by applying Bökstedt's original d…
The Morita equivalence between parametrized spectra and module spectra
John A. Lind, Cary Malkiewich
We give a Quillen equivalence between May and Sigurdsson's model category of parametrized spectra over BG, and Mandell, May, Schwede, and Shipley's model category of modules over t…