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- W2017658521 abstract "In this paper we consider the action of a finite group G on the geometric realization | CP | of the order complex CP of a poset P , on which a group G acts as a group of poset automorphisms. For special cases we give the G -homotopy type of | CP |. Moreover, we provide conditions which imply that the orbit space | CP vb/ G is homotopy equivalent to the geometric realization of the order complex over the orbit poset P G . The poset P G is the set of orbits [ x ] ≔ { x g | g ϵ G } of G in P ordered by [x] ≤ [y]: → ℶg ϵ G: x g ≤ y . We apply all our results to the case P = Λ ( G ) 0 is the lattice of subgroups H ≠ 1, G of a finite group G . For finite solvable groups G we give the G -homotopy type of Λ ( G ) 0 and we show that | CΛ ( G ) 0 |/ G and | C ( Λ ( G ) 0 / G )| are homotopy equivalent. We do the same for a class of direct products of finite groups and for some examples of simple groups. Finally we show that for the Mathieu group G = M 12 the orbit space | CΛ ( G ) 0 |/ G and | C ( Λ ( G ) 0 / G )| are not homotopy equivalent." @default.
- W2017658521 created "2016-06-24" @default.
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- W2017658521 date "1995-01-01" @default.
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- W2017658521 title "Equivariant homotopy of posets and some applications to subgroup lattices" @default.
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- W2017658521 doi "https://doi.org/10.1016/0097-3165(95)90107-8" @default.
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