Conley index and tubular neighborhoods II

This paper is a sequel to our previous paper [11]. We prove existence of nested index filtrations for tubular singular semiflow perturbations. This generalizes a corresponding result from [7] and is applicable to cases in which the phase space of the perturbed semiflow is not necessarily homeomorphic to a product of metric spaces having as a factor the phase space of the limiting semiflow. This result implies tubular homology index braid and connection matrix continuation principles.