38 citations · 125 across the 18 of their papers we have counts for
21 papers
Homology manifolds via six functor formalisms
Markus Land, Marco Volpe
We study homology manifolds through the eyes of the six functor formalism of spectral sheaves on locally compact Hausdorff spaces. As main results, we characterize cohomologically…
On the -theory of pushouts
Markus Land, Georg Tamme
We reveal a relation between the behaviour of localizing invariants on pushouts and on pullbacks of ring spectra. More concretely, we show that the failure of sending a pus…
L-theory of -algebras
Markus Land, Thomas Nikolaus, Marco Schlichting
We establish a formula for the L-theory spectrum of real -algebras from which we deduce a presentation of the L-groups in terms of the topological K-groups, extending all prev…
Gabber rigidity in hermitian K-theory
Markus Land
We note that Gabber's rigidity theorem for the algebraic K-theory of henselian pairs also holds true for hermitian K-theory with respect to arbitrary form parameters.
Remarks on chromatically localised hermitian K-theory
Markus Land
We describe chromatic localisations of genuine L-spectra of discrete rings and deduce that the purity property of -local -theory of rings established by Bhatt-Clausen-Math…
Paschke duality and assembly maps
Ulrich Bunke, Alexander Engel, Markus Land
We construct a natural transformation between two versions of -equivariant -homology with coefficients in a --category for a countable discrete group . Its domai…
A stable -category for equivariant -theory
Ulrich Bunke, Alexander Engel, Markus Land
For a countable group we construct a small, idempotent complete, symmetric monoidal, stable -category whose homotopy category recovers…
Hermitian K-theory for stable -categories III: Grothendieck-Witt groups of rings
Baptiste Calmès, Emanuele Dotto, Yonatan Harpaz +6
We establish a fibre sequence relating the classical Grothendieck-Witt theory of a ring to the homotopy -orbits of its K-theory and Ranicki's original (non-period…
Hermitian K-theory for stable -categories II: Cobordism categories and additivity
Baptiste Calmès, Emanuele Dotto, Yonatan Harpaz +6
We define Grothendieck-Witt spectra in the setting of Poincaré -categories and show that they fit into an extension with a K- and an L-theoretic part. As consequences we de…
Topological 4-manifolds with 4-dimensional fundamental group
Daniel Kasprowski, Markus Land
Let be a group satisfying the Farrell-Jones conjecture and assume that is a 4-dimensional Poincaré duality space. We consider topological, closed, connected manifolds with…
On the homotopy type of L-spectra of the integers
Fabian Hebestreit, Markus Land, Thomas Nikolaus
We show that quadratic and symmetric L-theory of the integers are related by Anderson duality and show that both spectra split integrally into the L-theory of the real numbers and…
Purity in chromatically localized algebraic -theory
Markus Land, Akhil Mathew, Lennart Meier +1
We prove a purity property in telescopically localized algebraic -theory of ring spectra: For , the -localization of only depends on the $T(0)\oplus \dots…
Topologically flat embedded 2-spheres in specific simply connected 4-manifolds
Daniel Kasprowski, Peter Lambert-Cole, Markus Land +1
In this note we study whether specific elements in the second homology of specific simply connected closed -manifolds can be represented by smooth or topologically flat embedded…
Connected sum decompositions of high-dimensional manifolds
Imre Bokor, Diarmuid Crowley, Stefan Friedl +4
The classical Kneser-Milnor theorem says that every closed oriented connected 3-dimensional manifold admits a unique connected sum decomposition into manifolds that cannot be decom…
On the K-theory of pullbacks
Markus Land, Georg Tamme
To any pullback square of ring spectra we associate a new ring spectrum and use it to describe the failure of excision in algebraic -theory. The construction of this new ring sp…
Reducibility of low dimensional Poincaré duality spaces
Markus Land
We discuss Poincaré duality complexes X and the question whether or not their Spivak normal fibration admits a reduction to a vector bundle in the case where the dimension of X is…
A vanishing theorem for tautological classes of aspherical manifolds
Fabian Hebestreit, Markus Land, Wolfgang Lück +1
Tautological classes, or generalised Miller-Morita-Mumford classes, are basic characteristic classes of smooth fibre bundles, and have recently been used to describe the rational c…
Localization of Cofibration Categories and Groupoid -algebras
Markus Land, Thomas Nikolaus, Karol Szumiło
We prove that relative functors out of a cofibration category are essentially the same as relative functors which are only defined on the subcategory of cofibrations. As an applica…
On the Relation between K- and L-Theory of -Algebras
Markus Land, Thomas Nikolaus
We prove the existence of a map of spectra between connective topological K-theory and connective algebraic L-theory of a complex -algebra A which is na…
Stable classification of 4-manifolds with 3-manifold fundamental groups
Daniel Kasprowski, Markus Land, Mark Powell +1
We study closed, oriented 4-manifolds whose fundamental group is that of a closed, oriented, aspherical 3-manifold. We show that two such 4-manifolds are stably diffeomorphic if an…
The Analytical Assembly Map and Index Theory
Markus Land
In this paper we study the index theoretic interpretation of the analytical assembly map that appears in the Baum-Connes conjecture. In its general form it may be constructed using…