On weak shape equivalences
نویسندگان
چکیده
منابع مشابه
Equivariant weak n-equivalences
The notion of n-type was introduced by J.H.C. Whitehead ([22, 23]) where its clear geometric meaning was presented. Following J.L. Hernandez and T. Porter ([12, 13]) we use the term weak n-equivalence for a map f : X → Y of path-connected spaces which induces isomorphisms πk(f) : πk(X)→ πk(Y ) on homotopy groups for k ≤ n. Certainly, weak n-equivalence of a map determines its n-connectedness bu...
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Weak equivalences of simplicial presheaves are usually defined in terms of sheaves of homotopy groups. We give another characterization using relative-homotopy-liftings, and develop the tools necessary to prove that this agrees with the usual definition. From our lifting criteria we are able to prove some foundational (but new) results about the local homotopy theory of simplicial presheaves.
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We extend the notion of shape-Wilf-equivalence to vincular patterns (also known as “generalized patterns” or “dashed patterns”). First we introduce a stronger equivalence on patterns which we call filling-shape-Wilfequivalence. When vincular patterns α and β are filling-shape-Wilf-equivalent, we prove that α⊕ σ and β ⊕ σ must also be filling-shape-Wilf-equivalent. We also discover two new pairs...
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 1999
ISSN: 0166-8641
DOI: 10.1016/s0166-8641(97)00252-6