Symplectic Groups Are N - Determined 2 - Compact Groups

نویسنده

  • ANTONIO VIRUEL
چکیده

We show that for n ≥ 3 the symplectic group Sp(n) is as a 2-compact group determined up to isomorphism by the isomorphism type of its maximal torus normalizer. This allows us to determine the integral homotopy type of Sp(n) among connected finite loop spaces with maximal torus.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Lattices in contact Lie groups and 5-dimensional contact solvmanifolds

This paper investigates the geometry of compact contact manifolds that are uniformized by contact Lie groups, i.e., manifolds of the form Γ \ G for some Lie group G with a left invariant contact structure and uniform lattice Γ ⊂ G. We re-examine Alexander’s criteria for existence of lattices on solvable Lie groups and apply them, along with some other well known tools. In particular, we restric...

متن کامل

Universality of Holomorphic Discrete Series

The goal here is to recover an apocryphal result on the structure of holomorphic discrete series representations of symplectic groups Spn(R) and unitary groups U(p, q) for sufficiently high highest weight of the lowest K-type. The same sort of argument applies to other groups of hermitian type, for example the classical groups O(n, 2) and O∗(2n). For Sp(n), the maximal compact is isomorphic to ...

متن کامل

On Some Examples in Symplectic Topology

Article is devoted to the Examples 2 and 3 of the symplectic solvable Lie groups R with some special cohomological properties, which have been constructed by Benson and Gordon. But they are not succeeded in constructing corresponding compact forms for symplectic structures on these Lie groups. Recently A.Tralle proved that there is no compact form in the Example 3. But his proof is rather compl...

متن کامل

Twisted Conjugacy Classes in Symplectic Groups, Mapping Class Groups and Braid Groups

We prove that the symplectic group Sp(2n,Z) and the mapping class group ModS of a compact surface S satisfy the R∞ property. We also show that Bn(S), the full braid group on n-strings of a surface S, satisfies the R∞ property in the cases where S is either the compact disk D, or the sphere S. This means that for any automorphism φ of G, where G is one of the above groups, the number of twisted ...

متن کامل

ar X iv : 0 90 6 . 43 97 v 1 [ m at h . G R ] 2 4 Ju n 20 09 Locally Compact Abelian Groups with symplectic self - duality

Is every locally compact abelian group which admits a symplectic self-duality isomorphic to the product of a locally compact abelian group and its Pontryagin dual? Several sufficient conditions, covering all the typical applications are found. Counterexamples are produced by studying a seemingly unrelated question about the structure of maximal isotropic subgroups of finite abelian groups with ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2008