1,560 research outputs found
Cohomology of Split Group Extensions and Characteristic Classes
There are characteristic classes that are the obstructions to the vanishing
of the differentials in the Lyndon-Hochischild-Serre spectral sequence of an
extension of an integral lattice L by a group G. These characteristic classes
exist in a given page of the spectral sequence provided the differentials in
the previous pages are all zero. When L decomposes into a sum of G-sublattices,
we show that there are defining relations between the characteristic classes of
L and the characteristic classes of its summands.Comment: 13 page
Crystallographic actions on contractible algebraic manifolds
We study properly discontinuous and cocompact actions of a discrete subgroup
of an algebraic group on a contractible algebraic manifold . We
suppose that this action comes from an algebraic action of on such that
a maximal reductive subgroup of fixes a point. When the real rank of any
simple subgroup of is at most one or the dimension of is at most three,
we show that is virtually polycyclic. When is virtually
polycyclic, we show that is virtually polycyclic. When is
virtually polycyclic, we show that the action reduces to a NIL-affine
crystallographic action. As applications, we prove that the generalized
Auslander conjecture for NIL-affine actions holds up to dimension six and give
a new proof of the fact that every virtually polycyclic group admits a
NIL-affine crystallographic action.Comment: This final version has been accepted for publication in 2013. The
statements of the main results are now more general as they cover algebraic
groups G where the real rank of any simple subgroup of G is at most on
Science, Bourgeois Dignity, and the Industrial Revolution
What happened to make for the factor of 16 were new ideas, what Mokyr calls “industrial Enlightenment.” But the Scientific Revolution did not suffice. Non-Europeans like the Chinese outstripped the West in science until quite late. Britain did not lead in science---yet clearly did in technology. Indeed, applied technology depended on science only a little even in 1900.scientific revolution, science, technology, industrial enlightenment, applied technology
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