17,757 research outputs found
Classifying -algebras with both finite and infinite subquotients
We give a classification result for a certain class of -algebras
over a finite topological space in which there exists an
open set of such that separates the finite and infinite
subquotients of . We will apply our results to -algebras
arising from graphs.Comment: Version III: No changes to the text. We only report that Lemma 4.5 is
not correct as stated. See arXiv:1505.05951 for the corrected version of
Lemma 4.5. As noted in arXiv:1505.05951, the main results of this paper are
true verbatim. Version II: Improved some results in Section 3 and loosened
the assumptions in Definition 4.
Enclosings of Decompositions of Complete Multigraphs in -Edge-Connected -Factorizations
A decomposition of a multigraph is a partition of its edges into
subgraphs . It is called an -factorization if every
is -regular and spanning. If is a subgraph of , a
decomposition of is said to be enclosed in a decomposition of if, for
every , is a subgraph of .
Feghali and Johnson gave necessary and sufficient conditions for a given
decomposition of to be enclosed in some -edge-connected
-factorization of for some range of values for the parameters
, , , , : , and either ,
or and and , or and . We generalize
their result to every and . We also give some
sufficient conditions for enclosing a given decomposition of in
some -edge-connected -factorization of for every
and , where is a constant that depends only on ,
and~.Comment: 17 pages; fixed the proof of Theorem 1.4 and other minor change
Hurwitz equivalence of braid monodromies and extremal elliptic surfaces
We discuss the equivalence between the categories of certain ribbon graphs
and subgroups of the modular group and use it to construct
exponentially large families of not Hurwitz equivalent simple braid monodromy
factorizations of the same element. As an application, we also obtain
exponentially large families of {\it topologically} distinct algebraic objects
such as extremal elliptic surfaces, real trigonal curves, and real elliptic
surfaces
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