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24-09-2016, 23:08
Ημερομηνία: Τετάρτη 28 Σεπτεμβρίου 2016
Τόπος: Αίθουσα 342 κτίριο Βιολογίας/Μαθηματικών
Ώρα: 13:00 - 14:00
Ομιλητής: Dmitri Alekseevsky, Institute for Information Transmission Problems, Russian Acad. Sci.
Τίτλος: Spinor structures on compact homogeneous manifolds


We study spin structures on compact simply-connected homogeneous pseudo-Riemannian manifolds (M = G/H,g) of a compact semisimple Lie group G. The existence of spin structure on a such manifold does not depend onmetric and is equivalent to vanishing of the second Stiefel-Whitney class w_2(M). Moreover, if the manifold M admits a complex structure J, then this condition is equivalent to the condition that the first Chern class c_1(M,J) ∈ H_2(M,Z) is even.
For a flag manifold F = G/H , the parity of c_1(F,J) does not depend on invariant complex structure. We calculate c_1(F,J) for some "standard" invariant
complex structure for all flag manifolds F = G/H where G is a simple compact Lie group (classical or exceptional). This gives a classifcation of
all spin flag manifolds. We apply this result to description of C-spaces (i.e. homogeneous torus bundles over flag manifolds) which admit spin structure. The talk is based on a joint work with Ioannis Chrysikos.