On Quillen's Fiber Lemma

JONATHAN ARIEL BARMAK

Abisko

Workshop; Aurora Borealis Combinatorics Workshop; 2010

p { margin-bottom: 0.21cm; } In this talk I will give an elementary proof of the result in the title, using the theory of finite topological spaces. The advantage of this proof is also that it can be easily modified to obtain a stronger simple homotopy version of the lemma. This, in turn, provides stronger formulations of well known results as the Nerve Lemma, Rota Cross-cut Theorem and Dowker’s Theorem.