منابع مشابه
Remarks on Finite Subset Spaces
This paper expands on and refines some known and less well-known results about the finite subset spaces of a simplicial complex X including their connectivity and manifold structure. It also discusses the inclusion of the singletons into the threefold subset space and shows that this subspace is weakly contractible but generally non-contractible unless X is a cogroup. Some homological calculati...
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Given a topological space X denote by expkX the space of non-empty subsets of X of size at most k , topologised as a quotient of X . This space may be regarded as a union over 1 ≤ l ≤ k of configuration spaces of l distinct unordered points in X . In the special case X = S we show that: (1) expkS 1 has the homotopy type of an odd dimensional sphere of dimension k or k − 1; (2) the natural inclu...
متن کاملFinite subset spaces of closed surfaces
The kth finite subset space of a topological space X is the space expkX of non-empty finite subsets of X of size at most k , topologised as a quotient of X . The construction is a homotopy functor and may be regarded as a union of configuration spaces of distinct unordered points in X . We show that the finite subset spaces of a connected 2–complex admit “lexicographic cell structures” based on...
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The kth finite subset space of a topological space X is the space expkX of non-empty subsets of X of size at most k, topologised as a quotient of X . Using results from our earlier paper on the finite subset spaces of connected graphs we show that if X is a connected cell complex then the homotopy group πi(expkX) vanishes for i ≤ k−2, and that if in addition X has finite dimension n then the ho...
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The k-th finite subset space of a topological space X is the space expkX of nonempty subsets of X of size at most k, topologised as a quotient of X. Using results from our earlier paper on the finite subset spaces of connected graphs we show that the k-th finite subset space of a connected cell complex is (k − 2)-connected, and (k − 1)-connected if in addition the underlying space is simply con...
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ژورنال
عنوان ژورنال: Algebraic & Geometric Topology
سال: 2002
ISSN: 1472-2739,1472-2747
DOI: 10.2140/agt.2002.2.1119