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A faithful linear-categorical action of the mapping class group of a surface with boundary

Robert Lipshitz, Peter Ozsváth, Dylan P. Thurston (2013)

Journal of the European Mathematical Society

We show that the action of the mapping class group on bordered Floer homology in the second to extremal spin c -structure is faithful. This paper is designed partly as an introduction to the subject, and much of it should be readable without a background in Floer homology.

A note on model structures on arbitrary Frobenius categories

Zhi-wei Li (2017)

Czechoslovak Mathematical Journal

We show that there is a model structure in the sense of Quillen on an arbitrary Frobenius category such that the homotopy category of this model structure is equivalent to the stable category ̲ as triangulated categories. This seems to be well-accepted by experts but we were unable to find a complete proof for it in the literature. When is a weakly idempotent complete (i.e., every split monomorphism is an inflation) Frobenius category, the model structure we constructed is an exact (closed)...

A representation theorem for certain Boolean lattices.

José Ríos Montes (1988)

Publicacions Matemàtiques

Let R be an associative ring with 1 and R-tors the somplete Brouwerian lattice of all hereditary torsion theories on the category of left R-modules. A well known result asserts that R is a left semiartinian ring iff R-tors is a complete atomic Boolean lattice. In this note we prove that if L is a complete atomic Boolean lattice then there exists a left semiartinian ring R such that L is lattice-isomorphic to R-tors.

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