Bounded G-theory with fibred control

We use filtered modules over a Noetherian ring and fibred bounded control on homomorphisms to construct a new kind of controlled algebra with applications in geometric topology. The theory here can be thought of as a "pushout" of the bounded K-theory with fibred control and the controlled G-theory constructed and used by the authors. This paper contains the non-equivariant theory including controlled excision theorems crucial for computations.

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