Cohomology of homogeneous spaces
نویسندگان
چکیده
منابع مشابه
On the Cohomology of Generalized Homogeneous Spaces
We observe that work of Gugenheim and May on the cohomology of classical homogeneous spaces G/H of Lie groups applies verbatim to the calculation of the cohomology of generalized homogeneous spaces G/H, where G is a finite loop space or a p-compact group and H is a “subgroup” in the homotopical sense. We are interested in the cohomology H∗(G/H ; R) of a generalized homogeneous space G/H with co...
متن کاملEquivariant Quantum Cohomology of Homogeneous Spaces
We prove a Chevalley formula for the equivariant quantum multiplication of two Schubert classes in the homogeneous variety X = G/P . As in the case when X is a Grassmannian ([Mi1]), this formula implies an algorithm to compute the structure constants of the equivariant quantum cohomology algebra of X.
متن کاملMorse functions and cohomology of homogeneous spaces
Morse functions are useful tool in revealing the geometric formation of its domain manifolds M. They define the handle decompositions of M from which the additive homologies H * (M) may be constructed. In these lectures two further questions were emphasized. (1) How to find a Morse function on a given manifold? (2) From Morse functions can one derive the multiplicative coho-mology rather than t...
متن کاملQuantum cohomology of minuscule homogeneous spaces
We study the quantum cohomology of (co)minuscule homogeneous varieties under a unified perspective. We show that three points Gromov-Witten invariants can always be interpreted as classical intersection numbers on auxiliary homogeneous varieties. Our main combinatorial tools are certain quivers, in terms of which we obtain a quantum Chevalley formula and a higher quantum Poincaré duality. In pa...
متن کاملQuantum cohomology of minuscule homogeneous spaces II : Hidden symmetries
We prove that the quantum cohomology ring of any minuscule or cominuscule homogeneous space, once localized at the quantum parameter, has a non trivial involution mapping Schubert classes to multiples of Schubert classes. This can be stated as a strange duality property for the Gromov-Witten invariants, which turn out to be very symmetric.
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: Bulletin of the American Mathematical Society
سال: 1963
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1963-10984-2