✦ LIBER ✦
A Homotopy Equivalence for Partition Posets Related to Liftings of Sn−1-Modules to Sn
✍ Scribed by Sheila Sundaram
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 146 KB
- Volume
- 94
- Category
- Article
- ISSN
- 0097-3165
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✦ Synopsis
We give a homotopy equivalence to explain an S n&1 -module isomorphism which occurs frequently in the homology of subposets of the partition lattice 6 n . The isomorphism in question is necessary for the existence of a lifting to S n of the S n&1 -module involved. It has also been observed in certain deformations of the free Lie algebra. The topological explanation allows us to generate further examples in subposets of 6 n . We show that, in these two contexts, it is often accompanied by an S n -action on the S n&1 -module occurring in the isomorphism. A well-known example is the lifting of the homology of 6 n&1 .