X(R)] is the energy of the field X in a 3-sphere
of radius R [much less than] [R.
A twisted Alexander polynomial was first defined in  for knots in the 3-sphere
, and Wada () generalized this work and showed how to define a twisted Alexander polynomial given only a presentation of a group and representations to Z and GL(V) where V is a finite dimensional vector space over a field.
But as we could not immediately support this claim with a counterexample, our colleagues asked if there might always exist centre-of-mass-like points in the 3-sphere
3]/A is the Poincare homology 3-sphere and the induced action of [A.
It appears that this is the simplest example of an integral homology 3-sphere that supports a smooth one fixed point action and has a vanishing Rochlin invariant.
3] is a closed integral homology 3-sphere with one fixed point action of [A.
It looks to the observer like an energy contained in a 3-sphere
, but it is actually a conic 4-dimensional structure intersecting the present, the surface of the 4-sphere.
Genus theory for 3-manifolds, on the other hand, was formulated in [Mor01] and [Mor12] for the cyclic case over an integral homology 3-sphere ([ZHS.
Mizusawa, On the Iwasawa invariants of a link in the 3-sphere, Kyushu J.
In this article, following the analogies between knots and primes ([Mor12]), we establish relative genus theory for a branched cover of rational homology 3-spheres ([QHS.
In this paper, we construct an invariant for two-component handlebody-links in a 3-sphere
2] x R and also on the case of a 3-sphere
generated as R[P.