497 citations · 1.3k across the 20 of their papers we have counts for
21 papers
Chern classes in equivariant bordism
Stefan Schwede
We introduce Chern classes in -equivariant homotopical bordism that refine the Conner-Floyd-Chern classes in the -cohomology of . For products of unitary groups,…
Global stable splittings of Stiefel manifolds
Stefan Schwede
We prove global equivariant refinements of Miller's stable splittings of the infinite orthogonal, unitary and symplectic groups, and more generally of the spaces , …
Splittings of global Mackey functors and regularity of equivariant Euler classes
Stefan Schwede
We establish natural splittings for the values of global Mackey functors at orthogonal, unitary and symplectic groups. In particular, the restriction homomorphisms between the orth…
Global algebraic K-theory
Stefan Schwede
We introduce a global equivariant refinement of algebraic K-theory; here `global equivariant' refers to simultaneous and compatible actions of all finite groups. Our construction t…
Proper equivariant stable homotopy theory
Dieter Degrijse, Markus Hausmann, Wolfgang Lück +2
This monograph introduces a framework for genuine proper equivariant stable homotopy theory for Lie groups. The adjective `proper' alludes to the feature that equivalences are test…
Homotopy invariance of convolution products
Steffen Sagave, Stefan Schwede
The purpose of this paper is to show that various convolution products are fully homotopical, meaning that they preserve weak equivalences in both variables without any cofibrancy…
Categories and orbispaces
Stefan Schwede
Constructing and manipulating homotopy types from categorical input data has been an important theme in algebraic topology for decades. Every category gives rise to a `classifying…
Global homotopy theory
Stefan Schwede
This book introduces a new context for global homotopy theory, i.e., equivariant homotopy theory with universal symmetries. Many important equivariant theories naturally exist not…
Orbispaces, orthogonal spaces, and the universal compact Lie group
Stefan Schwede
This paper identifies the homotopy theories of topological stacks and orbispaces with unstable global homotopy theory. At the same time, we provide a new perspective by interpretin…
Equivariant properties of symmetric products
Stefan Schwede
The filtration on the infinite symmetric product of spheres by the number of factors provides a sequence of spectra between the sphere spectrum and the integral Eilenberg-Mac Lane…
Topological triangulated categories
Stefan Schwede
In this paper we explain certain systematic differences between algebraic and topological triangulated categories. A triangulated category is algebraic if it admits a differential…
Algebraic versus topological triangulated categories
Stefan Schwede
The most commonly known triangulated categories arise from chain complexes in an abelian category by passing to chain homotopy classes or inverting quasi-isomorphisms. Such example…
Triangulated categories without models
Fernando Muro, Stefan Schwede, Neil Strickland
We exhibit examples of triangulated categories which are neither the stable category of a Frobenius category nor a full triangulated subcategory of the homotopy category of a stabl…
On the homotopy groups of symmetric spectra
Stefan Schwede
The symmetric spectra introduced by Hovey, Shipley and Smith are a convenient model for the stable homotopy category with a nice associative and commutative smash product on the po…
Formal groups and stable homotopy of commutative rings
Stefan Schwede
We explain a new relationship between formal group laws and ring spectra in stable homotopy theory. We study a ring spectrum denoted DB which depends on a commutative ring B and is…
Morita theory in abelian, derived and stable model categories
Stefan Schwede
This is a survey paper, based on lectures given at the Workshop on "Structured ring spectra and their applications" which took place January 21-25, 2002, at the University of Glasg…
Equivalences of monoidal model categories
Stefan Schwede, Brooke Shipley
We construct Quillen equivalences between the model categories of monoids (rings), modules and algebras over two Quillen equivalent model categories under certain conditions. This…
Classification of stable model categories
Stefan Schwede, Brooke Shipley
A stable model category is a setting for homotopy theory where the suspension functor is invertible. The prototypical examples are the category of spectra in the sense of stable ho…
Simplicial structures on model categories and functors
Charles Rezk, Stefan Schwede, Brooke Shipley
We produce a highly structured way of associating a simplicial category to a model category which improves on work of Dwyer and Kan and answers a question of Hovey. We show that mo…
A uniqueness theorem for stable homotopy theory
Stefan Schwede, Brooke Shipley
In this paper we study the global structure of the stable homotopy theory of spectra. We establish criteria for when the homotopy theory associated to a given stable model category…
Algebras and modules in monoidal model categories
Stefan Schwede, Brooke E. Shipley
We construct model category structures for monoids and modules in symmetric monoidal model categories which satisfy an extra axiom, the monoidal axiom, with applications to symmetr…