Projects in Mathematics Muenster

Research area B: Spaces and Operators
Unit B2: Topology

Further Projects
CRC 1442: Geometry: Deformation and Rigidity - C01: Automorphisms and embeddings of manifolds This project concerns the homotopical properties of spaces of smooth and topological automorphisms of manifolds, their classifying spaces and spaces of smooth and topological embeddings of manifolds. Known characteristic classes for manifold bundles will play an important role. It is conceivable that new ones will be constructed. The action of automorphisms and embeddings on finite subsets of manifolds, more precisely on the configuration category of a manifold, will be exploited. online

Research Interests

Research Interests

$\bullet$ Differential topology, algebraic $K$-and $L$-theory.
$\bullet$ Functor Calculus, Homotopy theory.

Selected Publications

Selected Publications of Michael Weiss

$\bullet$ M. Weiss and B. Williams. Automorphisms of manifolds and algebraic $K$-theory: Part {III}. Mem. Amer. Math. Soc., 231(1084):vi+110, 2014.

$\bullet$ A. Ranicki and M. Weiss. On the construction and topological invariance of the Pontryagin classes. Geom. Dedicata, 148(1):309–343, 2010.

$\bullet$ S. Galatius, U. Tillmann, I. Madsen, and M. Weiss. The homotopy type of the cobordism category. Acta Math., 202(2):195–239, 2009.

$\bullet$ I. Madsen and M. Weiss. The stable moduli space of Riemann surfaces: Mumford's conjecture. Ann. of Math. (2), 165(3):843–941, 2007.

$\bullet$ W. Dwyer, M. Weiss, and B. Williams. A parametrized index theorem for the algebraic $K$-theory Euler class. Acta Math., 190(1):1–104, 2003.

$\bullet$ T. G. Goodwillie and M. Weiss. Embeddings from the point of view of immersion theory. {II}. Geom. Topol., 3:103–118 (electronic), 1999.

$\bullet$ M. Weiss. Embeddings from the point of view of immersion theory. I. Geom. Topol., 3:67–101 (electronic), 1999.

$\bullet$ M. Weiss. Orthogonal calculus. Trans. Amer. Math. Soc., 347(10):3743–3796, 1995. See also Erratum, {\it Trans.\ Amer.\ Math.\ Soc.}, 350(2):851-855, 1998.

$\bullet$ M. Weiss and B. Williams. Automorphisms of manifolds and algebraic $K$-theory: {II}. J. Pure Appl. Algebra, 62(1):47–107, 1989.

$\bullet$ M. Weiss and B. Williams. Automorphisms of manifolds and algebraic $K$-theory: I. $K$-Theory, 1(6):575–626, 1988.

Current Publications

$\bullet $ Michael Weiss. Rational Pontryagin classes of Euclidean fiber bundles. J. Geom. Topol, 25(7):3351––3424, January 2022. doi:10.2140/gt.2021.25.3351.

$\bullet $ Michael S. Weiss. Configuration categories and homotopy automorphisms. Glasg. Math. J., 62(1):13–41, January 2020. doi:10.1017/s0017089518000502.

$\bullet $ Michael S. Weiss. Truncated operads and simplicial spaces. Tunisian Journal of Mathematics, 1(1):109–126, March 2019. doi:10.2140/tunis.2019.1.109.