A fibre-restricted Gottlieb group and its rational realization problem
نویسندگان
چکیده
منابع مشابه
THE DERIVED GROUP OF A SEIFERT FIBRE GROUP
Every Seifert Fibre Group is the lift of a Fuchsian group to the universal covering group of PSL (2,R). From this, we work out a form of presentation for such a group. With the calculation of the Euler number, we can establish the presentation of the derived group of a Seifert Fibre Group
متن کاملA Rational Obstruction to Be a Gottlieb Map
We investigate Gottlieb maps, which are maps f : E → B that induce the maps between the Gottlieb groups πn(f)|Gn(E) : Gn(E) → Gn(B) for all n, from a rational homotopy theory point of view. We will define the obstruction group O(f) to be a Gottlieb map and a numerical invariant o(f). It naturally deduces a relative splitting of E in certain cases. We also illustrate several rational examples of...
متن کاملthe derived group of a seifert fibre group
every seifert fibre group is the lift of a fuchsian group to the universal covering group of psl (2,r). from this, we work out a form of presentation for such a group. with the calculation of the euler number, we can establish the presentation of the derived group of a seifert fibre group
متن کاملCohomologically Symplectic Spaces: Toral Actions and the Gottlieb Group
Aspects of symplectic geometry are explored from a homotopical viewpoint. In particular, the question of whether or not a given toral action is Hamiltonian is shown to be independent of geometry. Rather, a new homotopical obstruction is described which detects when an action is Hamiltonian. This new entity, the AA-invariant, allows many results of symplectic geometry to be generalized to manifo...
متن کاملNeural networks, rational functions, and realization theory
The problem of parametrizing single hidden layer scalar neural net works with continuous activation functions is investigated A connection is drawn between realization theory for linear dynamical systems ratio nal functions and neural networks that appears to be new A result of this connection is a general parametrization of such neural networks in terms of strictly proper rational functions So...
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: 2015
ISSN: 0166-8641
DOI: 10.1016/j.topol.2015.05.066