Bena Tshishiku

activity

20112026

most citedCharacteristic classes of bundles of K3 manifolds and the Nielsen realization problem

8 citations · 31 across the 20 of their papers we have counts for

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20 papers · 1 filter

math.GT2026

Finite group actions on nonpositively curved 3-manifolds

Bena Tshishiku, Zhengyu Zou

We show that every orientation-preserving action of a finite group on a closed nonpositively curved 3-manifold preserves a nonpositively curved metric.

math.GT2026

Morse complexity of homology classes

Fedor Manin, Bena Tshishiku, Shmuel Weinberger

The Morse complexity of a manifold is the minimal number of handles required to build it. We explore the Morse complexity of manifolds, bordisms, and homology classes, proving nont…

math.GT2024

Rotation index, Milnor--Munkres--Novikov pairing, and group actions on manifolds

Mauricio Bustamante, Bena Tshishiku

We introduce an invariant of a pair of commuting invertible matrices that we call the rotation index. We apply this invariant, together with the Milnor--Munkres--Novikov pairing, t…

math.GT2023

Surface mapping class group actions on 3-manifolds

Alina Al Beaini, Lei Chen, Bena Tshishiku

For each circle bundle $S^{1} \to X \to Σ_{g}$ over a surface with genus $g \geq 2$ , there is a natural surjection $π : H o m e o^{+} (X) \to M o d (Σ_{g})$ . When $X$ is the unit tangent bundle $U Σ_{g}$ , it…

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.GT2023

Mapping class groups of circle bundles over a surface

Lei Chen, Bena Tshishiku

In this paper, we study the algebraic structure of mapping class group $M o d (X)$ of 3-manifolds $X$ that fiber as a circle bundle over a surface $S^{1} \to X \to S_{g}$ . T…

math.GT2022

Nielsen Realization for sphere twists on 3-manifolds

Lei Chen, Bena Tshishiku

For a 3-manifold M, the twist group Twist(M) is the subgroup of the mapping class group Mod(M) generated by twists about embedded 2-spheres. We study the Nielsen realization proble…

math.GT2021

Finite rigid sets and the separating curve complex

Junzhi Huang, Bena Tshishiku

For each closed surface of genus $g \geq 3$ , we find a finite subcomplex of the separating curve complex that is rigid with respect to incidence-preserving maps.

math.GT2021

Symmetries of exotic aspherical space forms

Mauricio Bustamante, Bena Tshishiku

We study finite group actions on smooth manifolds of the form $M #Σ$ , where $Σ$ is an exotic $n$ -sphere and $M$ is a closed aspherical space form. We give a classification result f…

math.GT2019

Symmetries of exotic negatively curved manifolds

Mauricio Bustamante, Bena Tshishiku

Let $N$ be a smooth manifold that is homeomorphic but not diffeomorphic to a closed hyperbolic manifold $M$ . In this paper, we study the extent to which $N$ admits as much symmetry…

math.GT2018

Arithmeticity of the monodromy of some Kodaira fibrations

Nick Salter, Bena Tshishiku

A question of Griffiths-Schmid asks when the monodromy group of an algebraic family of complex varieties is arithmetic. We resolve this in the affirmative for the class of algebrai…

math.GT2018

Realization problems for diffeomorphism groups

Kathryn Mann, Bena Tshishiku

We discuss recent results and open questions on the broad theme of (Nielsen) realization problems. Beyond realizing subgroups of mapping class groups, there are many other natural…

math.GT2017

Geometric cycles and characteristic classes of manifold bundles

Bena Tshishiku

We produce new cohomology for non-uniform arithmetic lattices $Γ < S O (p, q)$ using a technique of Millson--Raghunathan. From this, we obtain new characteristic classes of manifold bun…

math.GT2016

Characteristic classes of fiberwise branched surface bundles via arithmetic

Bena Tshishiku

This paper is about cohomology of mapping class groups from the perspective of arithmetic groups. For a closed surface $S$ of genus $g$ , the mapping class group $M o d (S)$ admits a w…

math.GT2015★ 7 cited

On the non-realizability of braid groups by diffeomorphisms

Nick Salter, Bena Tshishiku

For every compact surface $S$ of finite type (possibly with boundary components but without punctures), we show that when $n$ is sufficiently large there is no lift $σ$ of the surf…

math.GT2015

Hyperbolic groups with boundary an n-dimensional Sierpinski space

Jean-François Lafont, Bena Tshishiku

For n>6, we show that if G is a torsion-free hyperbolic group whose visual boundary is an (n-2)-dimensional Sierpinski space, then G=π_1(W) for some aspherical n-manifold W with no…

math.GT2014

Pontryagin classes of locally symmetric manifolds

Bena Tshishiku

In this note we compute low degree rational Pontryagin classes for every closed locally symmetric manifold of noncompact type. In particular, we answer the question: Which locally…

math.GT2014★ 3 cited

Cohomological obstructions to Nielsen realization

Bena Tshishiku

For a based manifold (M,*), the question of whether the surjection Diff(M,*) \rightarrow π_0 Diff(M,*) admits a section is an example of a Nielsen realization problem. This questio…

math.GT2012★ 1 cited

Duality properties of indicatrices of knots

Colin Adams, Dan Collins, Katherine Hawkins +3

The bridge index and superbridge index of a knot are important invariants in knot theory. We define the bridge map of a knot conformation, which is closely related to these two inv…

math.GT2011★ 4 cited

Planar and spherical stick indices of knots

Colin Adams, Dan Collins, Katherine Hawkins +3

The stick index of a knot is the least number of line segments required to build the knot in space. We define two analogous 2-dimensional invariants, the planar stick index, which…

Finite group actions on nonpositively curved 3-manifolds

Morse complexity of homology classes

Rotation index, Milnor--Munkres--Novikov pairing, and group actions on manifolds

Surface mapping class group actions on 3-manifolds

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

Mapping class groups of circle bundles over a surface

Nielsen Realization for sphere twists on 3-manifolds

Finite rigid sets and the separating curve complex

Symmetries of exotic aspherical space forms

Symmetries of exotic negatively curved manifolds

Arithmeticity of the monodromy of some Kodaira fibrations

Realization problems for diffeomorphism groups

Geometric cycles and characteristic classes of manifold bundles

Characteristic classes of fiberwise branched surface bundles via arithmetic

On the non-realizability of braid groups by diffeomorphisms

Hyperbolic groups with boundary an n-dimensional Sierpinski space

Pontryagin classes of locally symmetric manifolds

Cohomological obstructions to Nielsen realization

Duality properties of indicatrices of knots

Planar and spherical stick indices of knots

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