Prof. Dr. Markus LandMathematisches Institut der Universität München Email: Markus.Land@mathematik.uni-muenchen.de Tel: +49 (0)89 2180 4415 |
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I work in algebraic topology and homotopy theory with main current interest in algebraic and hermitian
algebraic K-theory and their relation to L-theory and the topology of manifolds.
Preprints
Towards the classification of DGAs with polynomial homology
Joint with Haldun Özgür Bayındır.
Grothendieck--Witt theory of derived schemes
Joint with Marc Hoyois.
Formality of E_n-algebras and cochains on spheres
Joint with Gijs Heuts.
Homology manifolds and euclidean bundles
Joint with Fabian Hebestreit, Michael Weiss, and Christoph Winges.
A survey on operator K-theory via homotopical algebra
Joint with Ulrich Bunke and Ulrich Pennig.
On the K-theory of pushouts
Joint with Georg Tamme.
Paschke duality and assembly maps
Joint with Ulrich Bunke and Alexander Engel.
A stable \infty-category for equivariant KK-theory
Joint with Ulrich Bunke and Alexander Engel.
Publications
Hermitian K-theory for stable infinity-categories III: Grothendieck-Witt groups of rings
accepted for publication at Ann. of Math.
Joint with Baptiste Calmès, Emanuele Dotto, Yonatan Harpaz, Fabian Hebestreit, Kristian Moi, Denis Nardin, Thomas Nikolaus, and Wolfgang Steimle.
Hermitian K-theory for stable infinity-categories II: Cobordism categories and additivity
accepted for publication at Acta Math.
Joint with Baptiste Calmès, Emanuele Dotto, Yonatan Harpaz, Fabian Hebestreit, Kristian Moi, Denis Nardin, Thomas Nikolaus, and Wolfgang Steimle.
Purity in chromatically localized algebraic K-theory
J. Amer. Math. Soc. 37 (2024) no. 4, 1011-1040.
Joint with Akhil Mathew, Lennart Meier, and Georg Tamme.
L-theory of C*-algebras
Proc. London Math. Soc. (3). 127 (2023), no. 5, 1451--1506.
Joint with Thomas Nikolaus and Marco Schlichting.
Gabber rigidity in hermitian K-theory
Proc. Roy. Soc. Edinburgh Sect. A 154 (2024), no. 6, 1842–1847.
Hermitian K-theory for stable infinity-categories I: Foundations
Selecta Math. (N.S.) 29 (2023) no. 1.
Joint with Baptiste Calmès, Emanuele Dotto, Yonatan Harpaz, Fabian Hebestreit, Kristian Moi, Denis Nardin, Thomas Nikolaus, and Wolfgang Steimle.
Reducibility of low dimensional Poincare duality spaces
Münster J. of Math. 15 (2022) 47--81
Topological 4-manifolds with 4-dimensional fundamental group
Glasgow Math. J. 64, (2022), no. 2, 454-461.
Joint with Daniel Kasprowski.
Topologically flat embedded 2-spheres in specific simply connected 4-manifolds
2019--20 MATRIX annals, 111-116, MATRIX Book Ser., 4, Springer, Cham, 2021.
Joint with Daniel Kasprowski, Peter Lambert-Cole, and Ana G. Lecuona.
Connected sum decompositions of high-dimensional manifolds
2019--20 MATRIX annals, 5-30, MATRIX Book Ser., 4, Springer, Cham, 2021.
Joint with Imre Bokor, Diarmuid Crowley, Stefan Friedl, Fabian Hebestreit, and Daniel Kasprowski.
On the homotopy type of L-spectra of the integers
J. Topol. 14, (2021), no. 1, 183--214.
Joint with Fabian Hebestreit and Thomas Nikolaus.
A vanishing theorem for tautological classes of aspherical manifolds
Geometry & Topology 25-1 (2021), 47--110.
Joint with Fabian Hebestreit, Wolfgang Lück, and Oscar Randal-Williams.
On the K-theory of pullbacks
Ann. of Math. (2) 190 (2019), no. 3, 877--930.
Joint with Georg Tamme.
On the relation between K- and L-theory of C*-algebras
Math. Ann. 371 (2018), no. 1-2, 517--563.
Joint with Thomas Nikolaus.
Localization of cofibration categories and groupoid C*-algebras
Algebr. Geom. Topol. 17 (2017), no. 5, 3007--3020.
Joint with Thomas Nikolaus and Karol Szumilo.
Stable classification of 4-manifolds with 3-manifold fundamental group
J. Topol. 10, (2017), no. 3, 827--881.
Joint with Daniel Kasprowski, Mark Powell, and Peter Teichner.
The analytical assembly map and index theory
J. Noncommut. Geom. 9 (2015), no. 2, 603--619.
Book
Introduction to Infinity-categories
Compact Textbooks in mathematics, Birkhäuser, Cham, 2021.