Emergence of the Witt group in the cellular lattice of rational spaces

Abstract

We give an embedding of a quotient of the Witt semigroup into the lattice of rational cellular classes represented by formal 2 2 -cones between S 2 n S^{2n} and the two-cell complex X n = S 2 n ∪ [ ι , ι ] e 4 n X_n=S^{2n}\cup _{[\iota ,\iota ]}e^{4n} ( n ≥ 1 n\geq 1 ).