8 research outputs found

    The rank filtration and Robinson’s complex

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    AbstractFor a functor from the category of finite sets to abelian groups, Robinson constructed a bicomplex in [A. Robinson, Gamma homology, Lie representations and E∞ multiplications, Invent. Math. 152 (2) (2003) 331–348] which computes the stable derived invariants of the functor as defined by Dold–Puppe in [A. Dold, D. Puppe, Homologie nicht-additiver Funktoren. Anwendungen., Ann. Inst. Fourier (Grenoble) 11 (1961) 201–312]. We identify a subcomplex of Robinson’s bicomplex which is analogous to a normalization and also computes these invariants. We show that this new bicomplex arises from a natural filtration of the functor obtained by taking left Kan approximations on subcategories of bounded cardinality

    An equivariant smash spectral sequence and an unstable box product

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    Liberal arts colleges: an overlooked opportunity?

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    The smaller, more intimate environment of liberal arts colleges shapes the experiences of the faculty as well as the students. As faculty members at three substantially different liberal arts colleges in different regions of the country, we would like to share our experiences with the broader mathematical community. This article is a brief overview of the opportunities, rewards, and challenges of working at a liberal arts college

    A homotopy theoretical generalization of the Bestvina-Brady construction

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    By using the notion of polyhedral products (X,A)^K, we recognise the Bestvina–Brady construction [4] as the fundamental group of the homotopy fibre of (S^1,*)^L-->S^1, where L is a flag complex. We generalise their construction by studying the homotopy fibre F of (S^1,*)^L--> (S^1,*)^K for an arbitrary simplicial complex L and K an (m-1)-dimensional simplex. For a particular class of simplicial complexes L, we describe the homology of F, its fixed points, and maximal invariant quotients for coordinate subgroups of Z^m. This generalises the work of Leary and Saadetoğlu [13] who studied the case when m=1