Manuel Krannich

activity

20172026

most citedMapping class groups of highly connected

(4 k + 2)

-manifolds

20 citations · 76 across the 21 of their papers we have counts for

collaborators

23 papers

math.AT2026

Some homotopy coherent finite group actions on spheres

Manuel Krannich, Oscar Randal-Williams

We provide some examples of homotopy coherent smooth finite group actions on spheres which do not arise from strict actions.

math.AT2025★ 1 cited

Framed configuration spaces and exotic spheres

Manuel Krannich, Alexander Kupers, Fadi Mezher

We determine when an exotic sphere $Σ$ of dimension $d \neq \equiv 1 (4)$ can be detected through the homotopy type of its truncated Disc-presheaf. The latter records the diagram of…

math.AT2025

Pontryagin-Weiss classes and a rational decomposition of spaces of homeomorphisms

Manuel Krannich, Alexander Kupers

We construct a rational homotopy pullback decomposition for variants of the classifying space of the group of homeomorphisms for a large class of manifolds. This has various applic…

math.DG2025

Isoparametric foliations and bounded geometry

Manuel Krannich, Alexander Lytchak, Marco Radeschi

We prove that there are only finitely many isoparametrically foliated closed connected Riemannian manifolds with bounded geometry, fixed dimension $n \neq = 5$ , and finite fundamental…

math.AT2024

Infinity-operadic foundations for embedding calculus

Manuel Krannich, Alexander Kupers

Motivated by applications to spaces of embeddings and automorphisms of manifolds, we consider a tower of $\infty$ -categories of truncated right-modules over a unital $\infty$ -opera…

math.GT2024

A note on homotopy and pseudoisotopy of diffeomorphisms of $4$ -manifolds

Manuel Krannich, Alexander Kupers

This note serves to record examples of diffeomorphisms of closed smooth $4$ -manifolds $X$ that are homotopic but not pseudoisotopic to the identity, and to explain why there are no…

math.GT2023

Mapping class groups of exotic tori and actions by $SL_{d} (Z)$

Mauricio Bustamante, Manuel Krannich, Alexander Kupers +1

We determine for which exotic tori $T$ of dimension $d \neq = 4$ the homomorphism from the group of isotopy classes of orientation-preserving diffeomorphisms of $T$ …

math.AT2022

Two remarks on spaces of maps between operads of little cubes

Geoffroy Horel, Manuel Krannich, Alexander Kupers

We record two facts on spaces of derived maps between the operads $E_{d}$ of little $d$ -cubes. Firstly, these mapping spaces are equivalent to the mapping spaces between the non-unit…

math.AT2022★ 4 cited

Stability of concordance embeddings

Thomas Goodwillie, Manuel Krannich, Alexander Kupers

We prove a stability theorem for spaces of smooth concordance embeddings. From it we derive various applications to spaces of concordance diffeomorphisms and homeomorphisms.

math.AT2022★ 1 cited

The Disc-structure space

Manuel Krannich, Alexander Kupers

We study the Disc-structure space $S_{\partial}^{Disc} (M)$ of a compact smooth manifold $M$ . Informally speaking, this space measures the difference between $M$ , together with it…

math.AT2021

Diffeomorphisms of discs and the second Weiss derivative of BTop(-)

Manuel Krannich, Oscar Randal-Williams

We compute the rational homotopy groups in degrees up to approximately $\frac{3}{2}$ d of the group of diffeomorphisms of a closed d-dimensional disc fixing the boundary. Based on…

math.GT2021★ 6 cited

Mapping class groups of simply connected high-dimensional manifolds need not be arithmetic

Manuel Krannich, Oscar Randal-Williams

It is well known that Sullivan showed that the mapping class group of a simply connected high-dimensional manifold is commensurable with an arithmetic group, but the meaning of "co…

math.GT2021

On Torelli groups and Dehn twists of smooth 4-manifolds

Manuel Krannich, Alexander Kupers

This note has two related but independent parts. Firstly, we prove a generalisation of a recent result of Gay on the smooth mapping class group of $S^{4}$ . Secondly, we give an alter…

math.AT2021★ 1 cited

Finiteness properties of automorphism spaces of manifolds with finite fundamental group

Mauricio Bustamante, Manuel Krannich, Alexander Kupers

Given a closed smooth manifold $M$ of even dimension $2 n \geq 6$ with finite fundamental group, we show that the classifying space $BDiff (M)$ of the diffeomorphism group of $M$ …

math.AT2021★ 3 cited

Embedding calculus for surfaces

Manuel Krannich, Alexander Kupers

We prove convergence of Goodwillie-Weiss' embedding calculus for spaces of embeddings into a manifold of dimension at most two, so in particular for diffeomorphisms between surface…

math.AT2020★ 6 cited

An $H P^{2}$ -bundle over $S^{4}$ with nontrivial $A^$ -genus

Manuel Krannich, Alexander Kupers, Oscar Randal-Williams

We explain the existence of a smooth $H P^{2}$ -bundle over $S^{4}$ whose total space has nontrivial $A^$ -genus. Combined with an argument going back to Hitchin, this answers a ques…

math.AT2020

Some Hermitian K-groups via geometric topology

Manuel Krannich, Alexander Kupers

We compute the first two symplectic quadratic K-theory groups of the integers, or equivalently, the first two stable homology groups of the group of symplectic integral matrices pr…

math.AT2020★ 12 cited

A homological approach to pseudoisotopy theory. I

Manuel Krannich

We construct a zig-zag from the once delooped space of pseudoisotopies of a closed $2 n$ -disc to the once looped algebraic $K$ -theory space of the integers and show that the maps in…

math.AT2019★ 1 cited

A note on rational homological stability for automorphisms of manifolds

Manuel Krannich

By work of Berglund and Madsen, the rings of rational characteristic classes of fibrations and smooth block bundles with fibre $D^{2 n} ♯ (S^{n} \times S^{n})^{♯ g}$ , relative to…

math.AT2019★ 20 cited

Mapping class groups of highly connected $(4 k + 2)$ -manifolds

Manuel Krannich

We compute the mapping class group of the manifolds $♯^{g} (S^{2 k + 1} \times S^{2 k + 1})$ for $k > 0$ in terms of the automorphism group of the middle homology and the group of homotop…

math.AT2018★ 2 cited

Characteristic numbers of manifold bundles over surfaces with highly connected fibers

Manuel Krannich, Jens Reinhold

We study smooth bundles over surfaces with highly connected almost parallelizable fiber $M$ of even dimension, providing necessary conditions for a manifold to be bordant to the to…

math.AT2018★ 5 cited

On characteristic classes of exotic manifold bundles

Manuel Krannich

Given a closed simply connected manifold $M$ of dimension $2 n \geq 6$ , we compare the ring of characteristic classes of smooth oriented bundles with fibre $M$ to the analogous ring re…

math.AT2017★ 14 cited

Homological stability of topological moduli spaces

Manuel Krannich

Given a graded $E_{1}$ -module over an $E_{2}$ -algebra in spaces, we construct an augmented semi-simplicial space up to higher coherent homotopy over it, called its canonical resolution…

Some homotopy coherent finite group actions on spheres

Framed configuration spaces and exotic spheres

Pontryagin-Weiss classes and a rational decomposition of spaces of homeomorphisms

Isoparametric foliations and bounded geometry

Infinity-operadic foundations for embedding calculus

A note on homotopy and pseudoisotopy of diffeomorphisms of 4-manifolds

Mapping class groups of exotic tori and actions by SLd​(Z)

Two remarks on spaces of maps between operads of little cubes

Stability of concordance embeddings

The Disc-structure space

Diffeomorphisms of discs and the second Weiss derivative of BTop(-)

Mapping class groups of simply connected high-dimensional manifolds need not be arithmetic

On Torelli groups and Dehn twists of smooth 4-manifolds

Finiteness properties of automorphism spaces of manifolds with finite fundamental group

Embedding calculus for surfaces

An HP2-bundle over S4 with nontrivial A^-genus

Some Hermitian K-groups via geometric topology

A homological approach to pseudoisotopy theory. I

A note on rational homological stability for automorphisms of manifolds

Mapping class groups of highly connected (4k+2)-manifolds

Characteristic numbers of manifold bundles over surfaces with highly connected fibers

On characteristic classes of exotic manifold bundles

Homological stability of topological moduli spaces

A note on homotopy and pseudoisotopy of diffeomorphisms of $4$ -manifolds

Mapping class groups of exotic tori and actions by $SL_{d} (Z)$

An $H P^{2}$ -bundle over $S^{4}$ with nontrivial $A^$ -genus

Mapping class groups of highly connected $(4 k + 2)$ -manifolds