18 citations · 70 across the 19 of their papers we have counts for
21 papers
Weighted coloop splittings in rank six
James Dylan Douthitt, Lee Kennard, Josef Komissar
With a view toward applications in Riemannian geometry, we explore coloop splitting properties of regular matroids. Nienhaus showed by classification in rank four that a regular ma…
Higher cosystoles of matroids
James Dylan Douthitt, Elana Israel, Lee Kennard
We define a matroid invariant called the three-cosystole that is related to higher notions of cogirth for weighted matroids, and we prove an optimal upper bound for it in the class…
On Hopf's conjecture and positive second intermediate Ricci curvature
Lee Kennard, Lawrence Mouillé, Jan Nienhaus
Hopf conjectured that even-dimensional closed Riemannian manifolds with positive sectional curvature have positive Euler characteristic. The conclusion of the conjecture is known t…
Extending Adams' theorem from singly generated to periodic cohomology
John R. Harper, Lee Kennard
In 1960, J.F. Adams introduced secondary cohomology operations that are defined on cohomology elements on which sufficiently many Steenrod algebra elements vanish. This led to his…
Positive intermediate Ricci curvature with maximal symmetry rank
Lee Kennard, Lawrence Mouillé
Generalizing the foundational work of Grove and Searle, the second author proved upper bounds on the ranks of isometry groups of closed Riemannian manifolds with positive intermedi…
Positive curvature, torus symmetry, and matroids
Lee Kennard, Michael Wiemeler, Burkhard Wilking
We identify a link between regular matroids and torus representations all of whose isotropy groups have an odd number of components. Applying Seymour's 1980 classification of the f…
Positive curvature and discrete abelian symmetry
Lee Kennard, Elahe Khalili Samani, Catherine Searle
By replacing the torus with an elementary abelian two-group, we generalize the maximal symmetry result of Grove and Searle and the half-maximal symmetry result of Wilking for posit…
Splitting of torus representations and applications in the Grove symmetry program
Lee Kennard, Michael Wiemeler, Burkhard Wilking
A 1930s conjecture of Hopf states that an even-dimensional compact Riemannian manifold with positive sectional curvature has positive Euler characteristic. We prove this conjecture…
Halperin's conjecture in formal dimensions up to 20
Lee Kennard, Yantao Wu
A 1976 conjecture of Halperin on positively elliptic spaces was recently confirmed in formal dimensions up to 16. In this article, we shorten the proof and extend the result up to…
Cohomogeneity one manifolds with singly generated rational cohomology
Jason DeVito, Lee Kennard
We classify simply connected, closed cohomogeneity one manifolds with singly generated or 4-periodic rational cohomology and positive Euler characteristic.
The weighted connection and sectional curvature for manifolds with density
Lee Kennard, William Wylie, Dmytro Yeroshkin
In this paper we study sectional curvature bounds for Riemannian manifolds with density from the perspective of a weighted torsion free connection introduced recently by the last t…
On dimensions supporting a rational projective plane
Lee Kennard, Zhixu Su
A rational projective plane () is a simply connected, smooth, closed manifold such that . An open prob…
Positive curvature and torus symmetry in small dimensions, I -- Dimensions 10, 12, 14, and 16
Manuel Amann, Lee Kennard
This is the first part of a series of papers where we compute Euler characteristics, signatures, elliptic genera, and a number of other invariants of smooth manifolds that admit Ri…
Characterizations of the round two-dimensional sphere in terms of closed geodesics
Lee Kennard, Jordan Rainone
The question of whether a closed Riemannian manifold has infinitely many geometrically distinct closed geodesics has a long history. Though unsolved in general, it is well understo…
Positive weighted sectional curvature
Lee Kennard, William Wylie
In this paper, we give a new generalization of positive sectional curvature called positive weighted sectional curvature. It depends on a choice of Riemannian metric and a smooth v…
Positive curvature and rational ellipticity
Manuel Amann, Lee Kennard
Simply-connected manifolds of positive sectional curvature are speculated to have a rigid topological structure. In particular, they are conjectured to be rationally elliptic,…
On a generalized conjecture of Hopf with symmetry
Manuel Amann, Lee Kennard
A famous conjecture of Hopf is that the product of the two-dimensional sphere with itself does not admit a Riemannian metric with positive sectional curvature. More generally, one…
Fundamental groups of manifolds with positive sectional curvature and torus symmetry
Lee Kennard
In 1965, S.-S. Chern posed a question concerning the extent to which fundamental groups of manifolds admitting positive sectional curvature look like spherical space form groups. T…
Topological properties of positively curved manifolds with symmetry
Manuel Amann, Lee Kennard
Manifolds admitting positive sectional curvature are conjectured to have rigid homotopical structure and, in particular, comparatively small Euler charateristics. In this article,…
Positively curved metrics on symmetric spaces with large symmetry rank
Lee Kennard
We prove an obstruction at the level of rational cohomology in small degrees to the existence of positively curved metrics with large symmetry rank. The symmetry rank bound is loga…
On the Hopf Conjecture with Symmetry
Lee Kennard
The Hopf conjecture states that an even-dimensional, positively curved Riemannian manifold has positive Euler characteristic. We prove this conjecture under the additional assumpti…