منابع مشابه
Finite groups acting on 3–manifolds and cyclic branched coverings of knots
We are interested in finite groups acting orientation-preservingly on 3–manifolds (arbitrary actions, ie not necessarily free actions). In particular we consider finite groups which contain an involution with nonempty connected fixed point set. This condition is satisfied by the isometry group of any hyperbolic cyclic branched covering of a strongly invertible knot as well as by the isometry gr...
متن کاملBranched 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 کامل3-manifolds Which Admit Finite Group Actions
We prove several results which support the following conjectures: (1) Any smooth action of a finite group on a geometric 3-manifold can be conjugated to preserve the geometric structure. (2) Every irreducible closed 3-manifold M with infinite nx(M) is finitely covered by a Haken 3-manifold.
متن کاملFinite Group Actions on Kervaire Manifolds
Let M K be the Kervaire manifold: a closed, piecewise linear (PL) manifold with Kervaire invariant 1 and the same homology as the product S × S of spheres. We show that a finite group of odd order acts freely on M K if and only if it acts freely on S × S. If MK is smoothable, then each smooth structure on MK admits a free smooth involution. If k 6= 2 − 1, then M K does not admit any free TOP in...
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: Journal of Topology
سال: 2018
ISSN: 1753-8416
DOI: 10.1112/topo.12052