We prove that every homogeneous continuum is an open retract of a non-metric homogeneous indecomposable continuum. 0. Introduction. A continuum X is indecomposable if it cannot be written as the union of two proper subcontinua. Examples of 1-dimensional homogeneous indecomposable continua are the pseudo-arc and the solenoids. J. T. Rogers asked whether there is an example of a homogeneous indec...

We use tilting modules to study the structure of the tensor product of two simple modules for the algebraic group SL2, in positive characteristic, obtaining a twisted tensor product theorem for its indecomposable direct summands. Various other related results are obtained, and numerous examples are computed. Introduction We study the structure of L ⊗ L where L,L are simple modules for the algeb...

An uncountable collection of arcs in S is constructed, each member of which is wild precisely at its endpoints, such that the fundamental groups of their complements are non-trivial, pairwise non-isomorphic, and indecomposable with respect to free products. The fundamental group of the complement of a certain Fox-Artin arc is also shown to be indecomposable.

We construct new families of examples of (real) Anosov Lie algebras starting with algebraic units. We also give examples of indecomposable Anosov Lie algebras (not a direct sum of proper Lie ideals) of dimension 13 and 16, and we conclude that for every n ≥ 6 with n 6= 7 there exists an indecomposable Anosov Lie algebra of dimension n.

The tournament N5 can be obtained from the transitive tournament on {1, . . . , 5}, with the natural order, by reversing the edges between successive vertices. Tournaments that do not have N5 as a subtournament are said to omit N5. We describe the structure of tournaments that omit N5 and use this with Kruskal’s Tree Theorem to prove that this class of tournaments is well-quasi-ordered. The pro...

We show that Mildenhall’s theorem implies that the indecomposable higher Chow group of a self-product of an elliptic curve over the complex number field is infinite dimensional, if the elliptic curve is modular and defined over rational numbers. For the moment we cannot prove even the nontriviality of the indecomposable higher Chow group by a complex analytic method in this case.