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MIT Combinatorics Seminar

Unions And Intersections Of Leray Complexes

Gil Kalai, (Hebrew University of Jerusalem and Yale University)

Friday, September 16, 2005   4:30 pm    Room 2-142

ABSTRACT

A simplicial complex K is d-Leray if all reduced homology groups H_i(L)vanish when i is equal or greater than d for every induced subcomplex L or K.

I will discuss d-Leray complexes and how they appear in combinatorial geometry problems, and present the following recent result, which in a commutative algebra formulation, settles a conjecture by Terai.

If K is d-Leray and L is r-Leray than their union is (r+d+1)-Leray and their intersections is (r+d)-Leray.