Picking up from a surprising discovery made during our work on Sn-based topological insulators, project A08 will redirect its main focus to a fascinating new science case: the study of real-space obstructed quantum spin Hall insulators (QSHI). This novel type among the Z2 -non-trivial quantum materials is characterized – in analogy to the real-space obstructed atomic insulators – by a mismatch between the electronic charge centers and the ionic positions resulting in electronic multipoles. We recently synthesized and characterized the first incarnation of this kind – a triangular atom monolayer of indium dubbed indenene – and showed that orbital interference on the lattice triangle can produce a honeycomb connectivity reminiscent of graphene, yet, whose large spin orbit coupling (SOC) opens a topological gap and drives the system deep into the QSHI regime. In the upcoming funding period, we will synthesize and investigate indenene as well as other Group-III triangular monolayers on a variety of substrates, hereby systematically tuning the ratio be- tween inversion symmetry breaking (ISB) and atomic SOC, vital parameters to determine the sys- tems’ first and higher-order topology (QSHI vs HOTI). Based on state of the art molecular beam epitaxy (MBE) growth and surface spectroscopy techniques (AFM/STS/STS & ARPES), we will ex- tract the relevant topological identifiers, and ultimately span the topological phase diagram of 2D triangular monolayers within the experimentally accessible parameter space. Project A08 has been and continues to be developed in intimate collaboration with our bismuthene efforts in A10 and with theory in C05, and creates further synergies with projects A06, A09 and B07.