The strong program in embodied cognitive science
G Sanches de Oliveira - Phenomenology and the Cognitive Sciences, 2023 - Springer
A popular trend in the sciences of the mind is to understand cognition as embodied,
embedded, enactive, ecological, and so on. While some of the work under the label of …
embedded, enactive, ecological, and so on. While some of the work under the label of …
Smoothness conditions in cohomogeneity one manifolds
L Verdiani, W Ziller - Transformation Groups, 2022 - Springer
SMOOTHNESS CONDITIONS IN COHOMOGENEITY ONE MANIFOLDS Page 1 Transformation
Groups SMOOTHNESS CONDITIONS IN COHOMOGENEITY ONE MANIFOLDS L. VERDIANI∗ …
Groups SMOOTHNESS CONDITIONS IN COHOMOGENEITY ONE MANIFOLDS L. VERDIANI∗ …
Splitting of torus representations and applications in the Grove symmetry program
L Kennard, M Wiemeler, B Wilking - arXiv preprint arXiv:2106.14723, 2021 - arxiv.org
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 …
with positive sectional curvature has positive Euler characteristic. We prove this conjecture …
On the geometry of some equivariantly related manifolds
LF Cavenaghi, LD Sperança - … Mathematics Research Notices, 2020 - academic.oup.com
We provide geometric realizations of both classical and “exotic”-manifolds such as spheres,
Kervaire manifolds, bundles over spheres, homogeneous spaces, and connected sums …
Kervaire manifolds, bundles over spheres, homogeneous spaces, and connected sums …
Extra-twisted connected sum G_2-manifolds
J Nordström - arXiv preprint arXiv:1809.09083, 2018 - arxiv.org
We present a construction of closed 7-manifolds of holonomy G_2, which generalises
Kovalev's twisted connected sums by taking quotients of the pieces in the construction …
Kovalev's twisted connected sums by taking quotients of the pieces in the construction …
Cohomogeneity one manifolds with quasipositive curvature
D Wulle - Mathematische Annalen, 2024 - Springer
In this paper, we give a classification of cohomogeneity one manifolds admitting an invariant
metric with quasipositive sectional curvature except for two 7-dimensional families. The main …
metric with quasipositive sectional curvature except for two 7-dimensional families. The main …
On the moduli space of nonnegatively curved metrics on Milnor spheres
A Dessai - arXiv preprint arXiv:1712.08821, 2017 - arxiv.org
Let $ M $ be a Milnor sphere or, more generally, the total space of a linear $ S^ 3$-bundle
over $ S^ 4$ with $ H^ 4 (M;\mathbb {Q})= 0$. We show that the moduli space of metrics of …
over $ S^ 4$ with $ H^ 4 (M;\mathbb {Q})= 0$. We show that the moduli space of metrics of …
Manifolds that admit a double disk-bundle decomposition
Under mild topological restrictions, this article establishes that a smooth, closed, simply
connected manifold of dimension at most seven which can be decomposed as the union of …
connected manifold of dimension at most seven which can be decomposed as the union of …
Positive intermediate Ricci curvature with maximal symmetry rank
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 …
bounds on the ranks of isometry groups of closed Riemannian manifolds with positive …
Zero entropy on entire Grauert tubes
P Suárez-Serrato - arXiv preprint arXiv:2410.05685, 2024 - arxiv.org
On a real analytic Riemannian manifold a Grauert tube is an uniquely adapted complex
structure defined on the tangent bundle. It is called entire if it may be defined on the whole …
structure defined on the tangent bundle. It is called entire if it may be defined on the whole …