M. Wiemeler

activity

20092026

most citedExotic torus manifolds and equivariant smooth structures on quasitoric manifolds

32 citations · 167 across the 31 of their papers we have counts for

collaborators

31 papers

math.DG2026

Torus actions, almost non-negative curvature and fundamental groups

Michael Wiemeler

We show that purely topological torus symmetries impose strong restrictions on the fundamental groups of almost non-negatively curved closed manifolds and on their actions on highe…

math.GT2026

Riemannian foliations on CROSSes

Marco Radeschi, Lorenzo Scoffone, Michael Wiemeler

We classify Riemannian foliations of closed manifolds homotopy equivalent to CROSSes.

math.DG2023

Positively curved $10$ -manifolds with $T^{3}$ -symmetry

Anusha M. Krishnan, Michael Wiemeler

We show that closed, simply connected, positively curved 10-manifolds with effective, isometric actions of $3$ -dimensional tori are homotopy spheres or homotopy complex projective…

math.GT2023

On circle actions with exactly three fixed points

Michael Wiemeler

We study smooth, closed orientable $S^{1}$ -manifolds $M$ with exactly $3$ fixed points. We show that the dimension of $M$ is of the form $4 \cdot 2^{a}$ or $8 \cdot (2^{a} + 2^{b})$ with $a,b\g…

math.DG2022

Positive curvature, torus symmetry, and matroids

Lee Kennard, Michael Wiemeler, Burkhard Wilking

We identify a link between regular matroids and torus representations all of whose isotropy groups have an odd number of components. Applying Seymour's 1980 classification of the f…

math.GT2022★ 1 cited

Rigidity of elliptic genera for non-spin manifolds

Michael Wiemeler

We discuss the rigidity of elliptic genera for non-spin manifolds $M$ with $S^{1}$ -action. We show that if the universal covering of $M$ is spin, then the universal elliptic genus of…

math.DG2021★ 2 cited

Splitting of torus representations and applications in the Grove symmetry program

Lee Kennard, Michael Wiemeler, Burkhard Wilking

A 1930s conjecture of Hopf states that an even-dimensional compact Riemannian manifold with positive sectional curvature has positive Euler characteristic. We prove this conjecture…

math.DG2020★ 5 cited

On the homotopy type of the space of metrics of positive scalar curvature

Johannes Ebert, Michael Wiemeler

Let $M^{d}$ be a simply connected spin manifold of dimension $d \geq 5$ admitting Riemannian metrics of positive scalar curvature. Denote by $R^{+} (M^{d})$ the space of such me…

math.GT2020

Smooth classification of locally standard $T^{k}$ -manifolds

Michael Wiemeler

We study locally standard $T^{k}$ -manifolds $M$ . In particular, we study the case where there is a continuous section to the orbit map $π : M \to M / T$ . We give a classificatio…

math.AT2019★ 4 cited

Classification of rationally elliptic toric orbifolds

Michael Wiemeler

In this note we classify simply connected rationally elliptic compact toric orbifolds up to algebraic isomorphism.

math.DG2018★ 8 cited

Non-negatively curved GKM orbifolds

Oliver Goertsches, Michael Wiemeler

In this paper we study non-negatively curved and rationally elliptic GKM $_{4}$ manifolds and orbifolds. We show that their rational cohomology rings are isomorphic to the rational co…

math.DG2017★ 11 cited

On the topology of moduli spaces of non-negatively curved Riemannian metrics

Wilderich Tuschmann, Michael Wiemeler

We study spaces and moduli spaces of Riemannian metrics with non-negative Ricci or non-negative sectional curvature on closed and open manifolds. We construct, in particular, the f…

math.AT2017★ 8 cited

An equivariant Quillen theorem

Bernhard Hanke, Michael Wiemeler

A classical theorem due to Quillen (1969) identifies the unitary bordism ring with the Lazard ring, which classifies the universal one-dimensional commutative formal group law. We…

math.GT2016★ 3 cited

On moduli spaces of positive scalar curvature metrics on highly connected manifolds

Michael Wiemeler

Let $M$ be a simply connected spin manifold of dimension at least six which admits a metric of positive scalar curvature. We show that the observer moduli space of positive scalar…

math.DG2016★ 1 cited

Moduli spaces of invariant metrics of positive scalar curvature on quasitoric manifolds

Michael Wiemeler

We show that the higher homotopy groups of the moduli space of torus-invariant positive scalar curvature metrics on certain quasitoric manifolds are non-trivial.

math.GT2015★ 4 cited

A note on torus actions and the Witten genus

Michael Wiemeler

We show that the Witten genus of a string manifold $M$ vanishes, if there is an effective action of a torus $T$ on $M$ such that $dim T > b_{2} (M)$ . We apply this result to study grou…

math.GT2015★ 1 cited

Equivariantly homeomorphic quasitoric manifolds are diffeomorphic

Michael Wiemeler

In this note we prove that equivariantly homeomorphic quasitoric manifolds are diffeomorphic. As a consequence we show that up to finite ambiguity the diffeomorphism type of certai…

math.GT2015★ 2 cited

$S^{1}$ -equivariant bordism, invariant metrics of positive scalar curvature, and rigidity of elliptic genera

Michael Wiemeler

We construct geometric generators of the effective $S^{1}$ -equivariant Spin- (and oriented) bordism groups with two inverted. We apply this construction to the question of which $S^1…

math.DG2014

Differentiable stability and sphere theorems for manifolds and Einstein manifolds with positive scalar curvature

Wilderich Tuschmann, Michael Wiemeler

Leon Green obtained remarkable rigidity results for manifolds of positive scalar curvature with large conjugate radius and/or injectivity radius. Using $C^{k, α}$ convergence techni…

math.DG2014★ 27 cited

Torus orbifolds, slice-maximal torus actions and rational ellipticity

Fernando Galaz-Garcia, Martin Kerin, Marco Radeschi +1

In this work, it is shown that a simply-connected, rationally-elliptic torus orbifold is equivariantly rationally homotopy equivalent to the quotient of a product of spheres by an…

math.DG2014★ 3 cited

Positively curved GKM-manifolds

Oliver Goertsches, Michael Wiemeler

Let T be a torus of dimension at least k and M a T-manifold. M is a GKM_k-manifold if the action is equivariantly formal, has only isolated fixed points, and any k weights of the i…

math.DG2014★ 16 cited

Torus manifolds and non-negative curvature

Michael Wiemeler

A torus manifold $M$ is a $2 n$ -dimensional orientable manifold with an effective action of an $n$ -dimensional torus such that $M^{T} \neq = \emptyset$ . In this paper we discuss the clas…

math.GT2013★ 11 cited

Circle actions and scalar curvature

Michael Wiemeler

We construct metrics of positive scalar curvature on manifolds with circle actions. One of our main results is that there exist $S^{1}$ -invariant metrics of positive scalar curvature…

math.GT2012★ 2 cited

Every quasitoric manifold admits an invariant metric of positive scalar curvature

Michael Wiemeler

We prove that every quasitoric manifold admits an invariant metric of positive scalar curvature.

Torus actions, almost non-negative curvature and fundamental groups

Riemannian foliations on CROSSes

Positively curved 10-manifolds with T3-symmetry

On circle actions with exactly three fixed points

Positive curvature, torus symmetry, and matroids

Rigidity of elliptic genera for non-spin manifolds

Splitting of torus representations and applications in the Grove symmetry program

On the homotopy type of the space of metrics of positive scalar curvature

Smooth classification of locally standard Tk-manifolds

Classification of rationally elliptic toric orbifolds

Non-negatively curved GKM orbifolds

On the topology of moduli spaces of non-negatively curved Riemannian metrics

An equivariant Quillen theorem

On moduli spaces of positive scalar curvature metrics on highly connected manifolds

Moduli spaces of invariant metrics of positive scalar curvature on quasitoric manifolds

A note on torus actions and the Witten genus

Equivariantly homeomorphic quasitoric manifolds are diffeomorphic

S1-equivariant bordism, invariant metrics of positive scalar curvature, and rigidity of elliptic genera

Differentiable stability and sphere theorems for manifolds and Einstein manifolds with positive scalar curvature

Torus orbifolds, slice-maximal torus actions and rational ellipticity

Positively curved GKM-manifolds

Torus manifolds and non-negative curvature

Circle actions and scalar curvature

Every quasitoric manifold admits an invariant metric of positive scalar curvature

Positively curved $10$ -manifolds with $T^{3}$ -symmetry

Smooth classification of locally standard $T^{k}$ -manifolds

$S^{1}$ -equivariant bordism, invariant metrics of positive scalar curvature, and rigidity of elliptic genera