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

Award ID contains: 2104346

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. ; ; (, Groups, Geometry, and Dynamics)
    For each circle bundleS^{1}\to X\to\Sigma_{g}over a surface with genusg\ge2, there is a natural surjection\pi:\operatorname{Homeo}^{+}(X)\to\operatorname{Mod}(\Sigma_{g}). WhenXis the unit tangent bundleU\Sigma_{g}, it is well known that\pisplits. On the other hand,\pidoes not split when the Euler numbere(X)is not divisible by the Euler characteristic\chi(\Sigma_{g})by Chen and Tshishiku (2023). In this paper, we show that this homomorphism does not split in many cases where\chi(\Sigma_{g})dividese(X). 
    more » « less
    Free, publicly-accessible full text available May 29, 2026
  2. ; ; ; (, 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
  3. ; (, Michigan Mathematical Journal)
    Abstract. In this paper, we study the algebraic structure of mapping class group Mod(X) of 3-manifolds X that fiber as a circle bundle over a surface S1 → X → Sg. There is an exact sequence 1→H1(Sg)→Mod(X)→Mod(Sg)→1. We relate this to the Birman exact sequence and determine when this sequence splits. 
    more » « less
    Full Text Available