skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Explore Research Products in the PAR
It may take a few hours for recently added research products to appear in PAR search results.


  • Home
  • Search Results
  • Page 1 of 1

Search for: All records

Creators/Authors contains: "Kupers, Alexander"

Note: When clicking on a Digital Object Identifier (DOI) number, you will be taken to an external site maintained by the publisher. Some full text articles may not yet be available without a charge during the embargo (administrative interval).
What is a DOI Number?

Some links on this page may take you to non-federal websites. Their policies may differ from this site.

  1. ; ; ; (, Transactions of the American Mathematical Society, Series B)
    We determine for which exotic tori T \mathcal {T} of dimension d ≠<#comment/> 4 d\neq 4 the homomorphism from the group of isotopy classes of orientation-preserving diffeomorphisms of T \mathcal {T} to S L d ( Z ) \mathrm {SL}_d(\mathbf {Z}) given by the action on the first homology group is split surjective. As part of the proof we compute the mapping class group of all exotic tori T \mathcal {T} that are obtained from the standard torus by a connected sum with an exotic sphere. Moreover, we show that any nontrivial S L d ( Z ) \mathrm {SL}_d(\mathbf {Z}) -action on T \mathcal {T} agrees on homology with the standard action, up to an automorphism of S L d ( Z ) \mathrm {SL}_d(\mathbf {Z}) . When combined, these results in particular show that many exotic tori do not admit any nontrivial differentiable action by S L d ( Z ) \mathrm {SL}_d(\mathbf {Z}) . 
    more » « less
    Free, publicly-accessible full text available November 15, 2025
  2. ; ; (, Algebraic & Geometric Topology)
    null (Ed.)
    Full Text Available 
  3. ; ; (, Tunisian Journal of Mathematics)
    Full Text Available 
  4. ; ; ; (, International Mathematics Research Notices)
    Full Text Available 
  5. ; (, Forum of Mathematics, Pi)
    We completely describe the algebraic part of the rational cohomology of the Torelli groups of the manifolds $$\#^{g}S^{n}\times S^{n}$$ relative to a disc in a stable range, for $$2n\geqslant 6$$ . Our calculation is also valid for $2n=2$ assuming that the rational cohomology groups of these Torelli groups are finite-dimensional in a stable range. 
    more » « less
    Full Text Available 
  6. ; (, Forum of Mathematics, Sigma)
    Abstract The Torelli group of $$W_g = \#^g S^n \times S^n$$ is the group of diffeomorphisms of $$W_g$$ fixing a disc that act trivially on $$H_n(W_g;\mathbb{Z} )$$ . The rational cohomology groups of the Torelli group are representations of an arithmetic subgroup of $$\text{Sp}_{2g}(\mathbb{Z} )$$ or $$\text{O}_{g,g}(\mathbb{Z} )$$ . In this article we prove that for $$2n \geq 6$$ and $$g \geq 2$$ , they are in fact algebraic representations. Combined with previous work, this determines the rational cohomology of the Torelli group in a stable range. We further prove that the classifying space of the Torelli group is nilpotent. 
    more » « less
    Full Text Available 
  7. ; ; (, Publications mathématiques de l'IHÉS)
    We prove a new kind of stabilisation result, “secondary homological stability,” for the homology of mapping class groups of orientable surfaces with one boundary component. These results are obtained by constructing CW approximations to the classifying spaces of these groups, in the category of E2-algebras, which have no E2-cells below a certain vanishing line. 
    more » « less
    Full Text Available