A GEOMETRIC VERSION OF THE TWISTED NIL-GROUPS

OLIVEIRA, ADRIANO VEIGA DE (2022) A GEOMETRIC VERSION OF THE TWISTED NIL-GROUPS. Doctoral thesis, UIN SAIZU Purwokerto.

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Abstract

In this dissertation, a geometric definition of the reduced twisted nil-groups in K-theory is given. For a path-connected finite CW-complex X with a cellular map g ∶ X → X, the reduced twisted nil-group Nil ̃(X, g) is defined as a quotient of a free abelian group on the set of equivalence classes of g-twisted nil-pairs, which are elements that satisfy some homotopy nilpotent condition. It is also proved that, if g ∶ X → X is a homotopy equivalence with homotopy inverse denoted by g −1 ∶ X → X, then the geometric reduced twisted nil-groups Nil ̃(X, g) and Nil ̃(X, g−1) sit inside the geometric Whitehead group W h(T(g)) as orthogonal summands.

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