be a wedge of two circles,
, with
their
point of tangency. Let
be a doubly infinite sequence of tangent
circles, with points of tangency
,
.
Define
to be the map which sends each
to
and
wraps the circles alternately about
and
, preserving the
indicated orientations
- Prove that
is a covering space of
.
- Describe the groups
and
, in terms of generators and relations.
- Explain why one expects
to be isomorphic to a subgroup of
. Then give an explicit isomorphism, identifying the images of the
generators of
as products of generators of
.
- Let
be the inclusion map. Construct the
covering space of
which belongs to
.