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pro vyhledávání: '"Kupers, A"'
In the literature, there are two standard rank filtrations on $K$-theory: an ``unstable'' one which is traditionally defined through the homology of $GL_n$, and a ``stable'' one which was defined by Rognes using the simplicial structure on Waldhausen
Externí odkaz:
http://arxiv.org/abs/2501.01609
Publikováno v:
Comptes Rendus. Mathématique, Vol 359, Iss 2, Pp 149-154 (2021)
We explain the existence of a smooth $\mathbf{H} P^2$-bundle over $S^4$ whose total space has nontrivial $\hat{A}$-genus. Combined with an argument going back to Hitchin, this answers a question of Schick and implies that the space of Riemannian metr
Externí odkaz:
https://doaj.org/article/bee9e0a3abe040e0a32ba858f4aae9df
Autor:
Krannich, Manuel, Kupers, Alexander
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 $\infty$-operad $\mathcal{O}$. We study monoidality and naturality properties of thi
Externí odkaz:
http://arxiv.org/abs/2409.10991
In any category with a reasonable notion of cover, each object has a group of scissors automorphisms. We prove that under mild conditions, the homology of this group is independent of the object, and can be expressed in terms of the scissors congruen
Externí odkaz:
http://arxiv.org/abs/2408.08081
We prove that the groups of orientation-preserving homeomorphisms and diffeomorphisms of $\mathbb{R}^n$ are boundedly acyclic, in all regularities. This is the first full computation of the bounded cohomology of a transformation group that is not com
Externí odkaz:
http://arxiv.org/abs/2405.20395
Autor:
Krannich, Manuel, Kupers, Alexander
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 such examples when $X$ is orientable and its fundamental group is a f
Externí odkaz:
http://arxiv.org/abs/2402.16167
We determine for which exotic tori $\mathcal{T}$ of dimension $d\neq4$ the homomorphism from the group of isotopy classes of orientation-preserving diffeomorphisms of $\mathcal{T}$ to ${\rm SL}_d(\mathbb Z)$ given by the action on the first homology
Externí odkaz:
http://arxiv.org/abs/2305.08065
Autor:
Kupers, Alexander
We show that the first two $k$-invariants of $Top/O$ vanish and give some applications.
Comment: 5 pages, revised version to appear in Archiv der Mathematik
Comment: 5 pages, revised version to appear in Archiv der Mathematik
Externí odkaz:
http://arxiv.org/abs/2303.12854
Autor:
Krannich, Manuel1 krannich@kit.edu, Kupers, Alexander2 a.kupers@utoronto.ca
Publikováno v:
Forum of Mathematics, Pi. 12/13/2024, Vol. 12, p1-98. 98p.
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-unitary versions of $E_d$. Secondly, all endomorphisms of $E_d$ are automo
Externí odkaz:
http://arxiv.org/abs/2211.00908