Homotopy invariants of covers and KKM-type lemmas
نویسندگان
چکیده
منابع مشابه
Branched Cyclic Covers and Finite Type Invariants
This work identifies a class of moves on knots which translate to m-equivalences of the associated p-fold branched cyclic covers, for a fixed m and any p (with respect to the Goussarov-Habiro filtration). These moves are applied to give a flexible (if specialised) construction of knots for which the Casson-Walker-Lescop invariant (for example) of their p-fold branched cyclic covers may be readi...
متن کاملFinite Type Invariants of Cyclic Branched Covers
Given a knot in an integer homology sphere, one can construct a family of closed 3-manifolds (parametrized by the positive integers), namely the cyclic branched coverings of the knot. In this paper we give a formula for the the Casson-Walker invariants of these 3-manifolds in terms of residues of a rational function (which measures the 2-loop part of the Kontsevich integral of a knot) and the s...
متن کاملFINITE TYPE LINK HOMOTOPY INVARIANTS II: Milnor’s ¯µ-invariants
We define a notion of finite type invariants for links with a fixed linking matrix. We show that Milnor's link homotopy invariant ¯ µ(ijk) is a finite type invariant, of type 1, in this sense. We also generalize this approach to Milnor's higher order ¯ µ invariants and show that they are also, in a sense, of finite type. Finally, we compare our approach to another approach for defining finite t...
متن کامل0 Finite Type Link - Homotopy Invariants
An explicit polynomial in the linking numbers lij and Milnor's triple linking numbers µ(rst) on six component links is shown to be a well-defined finite type link-homotopy invariant. This solves a problem raised by B. Mellor and D. Thurston. An extension of our construction also produces a finite type link invariant which detects the invertibility for some links.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Algebraic & Geometric Topology
سال: 2016
ISSN: 1472-2739,1472-2747
DOI: 10.2140/agt.2016.16.1799