1,471 research outputs found
On representation varieties of 3-manifold groups
We prove universality theorems ("Murphy's Laws") for representation schemes
of fundamental groups of closed 3-dimensional manifolds. We show that germs of
SL(2,C)-representation schemes of such groups are essentially the same as germs
of schemes of over rational numbers.Comment: 28 page
On the order of countable graphs
A set of graphs is said to be independent if there is no homomorphism between
distinct graphs from the set. We consider the existence problems related to the
independent sets of countable graphs. While the maximal size of an independent
set of countable graphs is 2^omega the On Line problem of extending an
independent set to a larger independent set is much harder. We prove here that
singletons can be extended (``partnership theorem''). While this is the best
possible in general, we give structural conditions which guarantee independent
extensions of larger independent sets. This is related to universal graphs,
rigid graphs and to the density problem for countable graphs
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