- The geodesic complexity of n-dimensional Klein bottles(arXiv)
Abstract : The geodesic complexity of a metric space X is the smallest k for which there is a partition of X x X into ENRs E_0,…,E_k on each of which there is a continuous choice of minimal geodesic sigma(x_0,x_1) from x_0 to x_1. We prove that the geodesic complexity of an n-dimensional Klein bottle equals 2n. Its topological complexity remains unknown for n>2.
2.The Rational Hull of Rudin’s Klein Bottle (arXiv)
Abstract : In this note, a general result for determining the rational hulls of fibered sets in C2 is established. We use this to compute the rational hull of Rudin’s Klein bottle, the first explicit example of a totally real nonorientable surface in C2. In contrast to its polynomial hull, which was shown to contain an open set by the first author in 2012, its rational hull is shown to be two-dimensional. Using the same method, we also compute the rational hulls of some other surfaces in C2
3. n-dimensional Klein bottles(arXiv)
Author : Donald M. Davis
Abstract : An n-dimensional analogue of the Klein bottle arose in our study of topological complexity of planar polygon spaces. We determine its integral cohomology algebra and stable homotopy type, and give an explicit immersion and embedding in Euclidean space.
4. A Classification of Fundamental Group Elements Representing simple closed curves on the punctured Klein Bottle(arXiv)
Author : Daniel Gomez
Abstract : In this paper we provide a classification of fundamental group elements representing simple closed curves on the punctured Klein bottle, Similar to the Birman-Series classification of curves on the punctured torus. In the process, an explicit description of the mapping class group is given. We then apply this to give a counterexample the simple loop conjecture for representations from the Klein bottle group to PGL(2,R)