Grothendieck’s theorem on non-abelian $H^2$ and local-global principles
نویسندگان
چکیده
منابع مشابه
On the Non-Abelian Stokes Theorem
We present the non-Abelian Stokes theorem for the Wilson loop in various forms and discuss its meaning. Its validity has been recently questioned by Faber, Ivanov, Troitskaya and Zach. We demonstrate that all points of their criticism are based on mistakes in mathematics. Finally, we derive a variant of our formula for the Wilson loop in lattice regularization.
متن کاملA Local - Global Theorem on Periodic Maps
Abstract. Let ψ1, . . . , ψk be maps from Z to an additive abelian group with positive periods n1, . . . , nk respectively. We show that the function ψ1 + · · · + ψk is constant if ψ1(x) + · · · + ψk(x) equals a constant for |S| consecutive integers x where S = {r/ns : r = 0, . . . , ns −1; s = 1, . . . , k}. This local-global theorem extends a previous result [Math. Res. Lett. 11(2004), 187–19...
متن کاملNon-abelian Local Invariant Cycles
Let f be a degeneration of Kähler manifolds. The local invariant cycle theorem states that for a smooth fiber of the degeneration, any cohomology class, invariant under the monodromy action, rises from a global cohomology class. Instead of the classical cohomology, one may consider the non-abelian cohomology. This note demonstrates that the analogous non-abelian version of the local invariant c...
متن کاملOn the non-Abelian Stokes theorem in SU(2) gluodynamics
Nowadays, there are quite a few formulations of non-Abelian Stokes theorem (NAST) available (for review see, e.g., Ref. [1] and references therein). Generically there exist two principal approaches, the operator [2] and the pathintegral [3] one. We consider a new version of non-Abelian Stokes theorem [4] for SU(2) valued Wilson loops in the fundamental representation. The basic idea is to intro...
متن کاملGlobal and Local Uncertainty Principles for Signals on Graphs
Uncertainty principles such as Heisenberg’s provide limits on the time-frequency concentration of a signal, and constitute an important theoretical tool for designing and evaluating linear signal transforms. Generalizations of such principles to the graph setting can inform dictionary design for graph signals, lead to algorithms for reconstructing missing information from graph signals via spar...
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: Journal of the American Mathematical Society
سال: 1998
ISSN: 0894-0347,1088-6834
DOI: 10.1090/s0894-0347-98-00271-9