Discrete homogeneity and ends of manifolds
نویسندگان
چکیده
It is shown that a connected non-compact metrizable manifold of dimension ≥2 strongly discrete homogeneous if and only it has one end (in the sense Freudenthal compactification). In fact, we obtain an isotopic version this result, which answers question Piergallini [9].
منابع مشابه
Mazurkiewicz Manifolds and Homogeneity
It is proved that no region of a homogeneous locally compact, locally connected metric space can be cut by an Fσ-subset of a “smaller” dimension. The result applies to different finite or infinite topological dimensions of metrizable spaces. The classical Hurewicz-Menger-Tumarkin theorem in dimension theory says that connected topological n-manifolds (with or without boundary) are Cantor manifo...
متن کاملThree-Manifolds and Manifolds with Cylindrical Ends
Contents Introduction. 1 Chapter 1. Four-dimensional Theory. 4 1. Setup. 4 2. A slice theorem for singular connections. 9 3. Laplacians on forms. 17 Chapter 2. Three-dimensional Theory. 22 1. Setup. 22 2. The Chern-Simons functional. 24 3. The deformation complex. 27 Chapter 3. Singular connections on manifolds with cylindrical ends. 33 1. Setup. 33 2. The translation-invariant case. 35 3. Glob...
متن کاملEnds of Manifolds: Recent Progress
In this note we describe some recent work on ends of manifolds. In particular, we discuss progress on two different approaches to generalizing Siebenmann’s thesis to include manifolds with non-stable fundamental groups at infinity.
متن کاملEnds of groups and compact Kähler manifolds
Asking that a manifold admit a Kähler structure places swingeing restrictions on its topology. The best-known illustration of this comes from Hodge theory: one knows that when a complex structure on a manifold has a compatible symplectic structure, the decomposition of forms into Hodge types descends to cohomology, with far-reaching consequences. However, this turns out to be just the tip of th...
متن کاملDirac operators on manifolds with periodic ends
This paper studies Dirac operators on end-periodic spin manifolds of dimension at least 4. We provide a necessary and sufficient condition for such an operator to be Fredholm for a generic end-periodic metric. We make use of end-periodic Dirac operators to give an analytical interpretation of an invariant of non-orientable smooth 4-manifolds due to Cappell and Shaneson. From this interpretation...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Topology and its Applications
سال: 2023
ISSN: ['1879-3207', '0166-8641']
DOI: https://doi.org/10.1016/j.topol.2023.108614