ON THE SEMICHARACTERISTICS OF HOMOGENEOUS SPACES
Copyright policy )ON THE SEMICHARACTERISTICS OF HOMOGENEOUS SPACES
This paper analyzes the Kervaire semicharacteristic of homogeneous spaces G/H, \(k(G/H)=\dim H^{2*}(G/H; {\mathbb{Z}}_ 2) (mod 2)\). Particular attention is paid to the case \(G=SU(n)\), and for example, one result is the following Theorem: Let H be a connected simple Lie subgroup of SU(n) with dim(SU(n)/H) odd. Then either \(k(SU(n)/H)=0\) or SU(n)/H is a sphere. - A similar result holds for H connected and semisimple, but is more technical.
- University of Cologne Germany
Characteristic classes and numbers in differential topology, Homology and cohomology of homogeneous spaces of Lie groups, simple Lie subgroup, Kervaire semicharacteristic of homogeneous spaces
Characteristic classes and numbers in differential topology, Homology and cohomology of homogeneous spaces of Lie groups, simple Lie subgroup, Kervaire semicharacteristic of homogeneous spaces
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