11 citations · 11 across the 9 of their papers we have counts for
13 papers
Ropes have an even number of ends
Thomas O. Rot
On 13-01-2024 the annual wintersymposium of the Koninlijk Wiskundig Genootschap (KWG) was held in the academiegebouw in Utrecht. The symposium had the theme ``inzichtelijk abstract…
Non-linear proper Fredholm maps and the stable homotopy groups of spheres
Thomas O. Rot, Lauran Toussaint
We classify non-linear proper Fredholm maps between Hilbert spaces, up to proper homotopy, in terms of the stable homotopy groups of spheres. We show that there is a surjective map…
A geometric computation of cohomotopy groups in co-degree one
Michael Jung, Thomas O. Rot
Using geometric arguments, we compute the group of homotopy classes of maps from a closed -dimensional manifold to the -sphere for . Our work extends results fr…
The relative cup-length in local Morse cohomology
Thomas O. Rot, Maciej Starostka, Nils Waterstraat
Local Morse cohomology associates cohomology groups to isolating neighborhoods of gradient flows of Morse functions on (generally non-compact) Riemannian manifolds . We show tha…
The homotopy classification of proper Fredholm maps of index one
Alberto Abbondandolo, Thomas O. Rot
In a previous paper we classified the homotopy classes of proper Fredholm maps from an infinite dimensional Hilbert manifold to its model space in terms of a suitable version of fr…
On the transitivity of the group of orbifold diffeomorphisms
Federica Pasquotto, Thomas O. Rot
Consider a connected manifold of dimension at least two and the group of compactly supported diffeomorphisms that are compactly supported isotopic to the identity. This group acts…
Degree theory for orbifolds
Federica Pasquotto, Thomas O. Rot
In [3] Borzellino and Brunsden started to develop an elementary differential topology theory for orbifolds. In this paper we carry on their project by defining a mapping degree for…
Homotopy classes of proper maps out of vector bundles
Thomas O. Rot
In this paper we classify the homotopy classes of proper maps , where is a vector bundle over a compact Hausdorff space. As a corollary we compute the…
Homotopy invariance of the Conley index and local Morse homology in Hilbert spaces
Marek Izydorek, Thomas O. Rot, Maciej Starostka +2
In this paper we introduce a new compactness condition - Property (C) - for flows in (not necessary locally compact) metric spaces. For such flows a Conley type theory can be devel…
On the homotopy classification of proper Fredholm maps into a Hilbert space
Alberto Abbondandolo, Thomas O. Rot
We classify the homotopy classes of proper Fredholm maps from an infinite dimensional Hilbert manifold into its model space in terms of a suitable version of framed cobordism. Our…
The Morse-Bott inequalities, orientations, and the Thom isomorphism in Morse homology
Thomas O. Rot
The Morse-Bott inequalities relate the topology of a closed manifold to the topology of the critical point set of a Morse-Bott function defined on it. The Morse-Bott inequalities a…
Morse-Conley-Floer Homology
T. O. Rot, R. C. A. M. Vandervorst
For Morse-Smale pairs on a smooth, closed manifold the Morse-Smale-Witten chain complex can be defined. The associated Morse homology is isomorphic to the singular homology of the…
On periodic orbits in cotangent bundles of non-compact manifolds
J. B. van den Berg, F. Pasquotto, T. O. Rot +1
This paper is concerned with the existence of periodic orbits on energy hypersurfaces in cotangent bundles of Riemannian manifolds defined by mechanical Hamiltonians. In \cite{bpv}…