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|Title:||Homology decompositions of the loops on 1-stunted Borel constructions of C2 -actions|
|Source:||Gao, M., Wu, J. (2013-09-11). Homology decompositions of the loops on 1-stunted Borel constructions of C2 -actions. Algebraic and Geometric Topology 13 (6) : 3175-3201. ScholarBank@NUS Repository. https://doi.org/10.2140/agt.2013.13.3175|
|Abstract:||The Carlsson construction is a simplicial group whose geometric realization is the loop space of the 1-stunted reduced Borel construction. Our main results are: (i) given a pointed simplicial set acted upon by the discrete cyclic group C2 of order 2, if the orbit projection has a section, then the loop space on the geometric realization of the Carlsson construction has a mod 2 homology decomposition; (ii) in addition, if the reduced diagonal map of the C2 -invariant set is homologous to zero, then the pinched sets in the above homology decomposition themselves have homology decompositions in terms of the C2 -invariant set and the orbit space. Result (i) generalizes a previous homology decomposition of the second author for trivial actions. To illustrate these two results, we compute the mod 2 Betti numbers of an example.|
|Source Title:||Algebraic and Geometric Topology|
|Appears in Collections:||Staff Publications|
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