A Topological Obstruction to Existence of Quaternionic Plücker Map
نویسنده
چکیده
It is shown that there is no continuous map from the quaternionic Grassmannian Grk,n(k ≥ 2, n ≥ k + 2) to the quaternionic projective space HP ∞ such that the pullback of the first Pontryagin class of the tautological bundle over HP is equal to the first Pontryagin class of the tautological bundle over Grk,n. In fact some more precise statement is proved.
منابع مشابه
Rational maps and Kleinian groups
What are the possible topological forms for a conformal dynamical system? Part of the answer is provided by two theorems, due to Thurston, which employ iteration on Teichmüller space to construct rational maps and Kleinian groups of a given topological form. More precisely, the iteration either finds a geometric model or reveals a topological obstruction to its existence. This dichotomy stems f...
متن کاملPeriodic solutions of quaternionic-valued ordinary differential equations
This paper uses topological degree methods to prove the existence of periodic solutions of some quaternionic-valued ordinary differential equations. Mathematics Subject Classification (2000). 34C25, 11R52
متن کاملRational Points on Atkin-Lehner Quotients of Shimura Curves
We study three families of Atkin-Lehner quotients of quaternionic Shimura curves: X, X 0 (N), and X D+ 1 (N), which serve as moduli spaces of abelian surfaces with potential quaternionic multiplication (PQM) and level N structure. The arithmetic geometry of these curves is similar to, but even richer than, that of the classical modular curves. Two important differences are the existence of a no...
متن کاملComparison between Algebraic and Topological K-theory of Locally Convex Algebras
This paper is concerned with the algebraic K-theory of locally convex C-algebras stabilized by operator ideals, and its comparison with topological K-theory. We show that if L is locally convex and J a Fréchet operator ideal, then all the different variants of topological K-theory agree on the completed projective tensor product L⊗̂J , and that the obstruction for the comparison map K(L⊗̂J ) → K(...
متن کاملSymmetry protected Z2-quantization and quaternionic Berry connection with Kramers degeneracy
As for a generic parameter dependent hamiltonian with the time reversal (TR) invariance, a non Abelian Berry connection with the Kramers (KR) degeneracy are introduced by using a quaternionic Berry connection. This quaternionic structure naturally extends to the many body system with the KR degeneracy. Its topological structure is explicitly discussed in comparison with the one without the KR d...
متن کامل