Poset fiber theorems with applications

Anders Bjorner

Royal Institute of Technology (KTH)

September 18,
refreshments at 3:45pm


Our point of departure are three fiber theorems for posets from a 1978 paper by Quillen. These theorems, which have been very influential in topological combinatorics, concern how properties are transferred between two posets connected by a poset map under suitable conditions on the fibers (contractibility, k-connectivity, Cohen-Macaulayness).

I will begin with a review of basics in the area. Then I will describe generalizations and new applications of all three theorems. Among the applications are generalizations of the crosscut theorem for posets, and poset-theoretic constructions corresponding to the weighted Segre product and Rees construction for semigroup rings.

This is based on joint work with M. Wachs and V. Welker.

Speaker's Contact Info: bjorner(at-sign)math.kth.se

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