Often we come across 'decay topology' while doing data analysis in experimental particle physics. My guess is that it represents decay of a particle and how it decays and into what it decays.
Edit: I was reading about D*+ reconstruction and analysis strategy in a thesis by R S de Rooji (https://www.researchgate.net/publication/258809712_Prompt_D_production_in_proton-proton_and_lead-lead_collisions_measured_with_the_ALICE_experiment_at_the_CERN_Large_Hadron_Collider).
The exact lines were "... this chapter introduces the strategy for the $D^{*+}$ reconstruction via the $D^{*+}\rightarrow D^0 \pi^+_{soft} \rightarrow K^-\pi^+\pi^+_{soft}$ hadronic decay channel. Furthermore, the decay topology defines a multitude of observables on which can be cut in order to increase the statistical significance of the $D^{*+}$ signal compared to the combinatorial background which arises from uncorrelated pairs of tracks."
[decay=(of a radioactive substance, particle, etc.) undergo change to a different form by emitting radiation. topology=the way in which constituent parts are interrelated or arranged.]
