We report on spectroscopic information and lifetime measurements in the neutron-rich <math><mmultiscripts><mi mathvariant="normal">I</mi><mprescripts/><none/><mrow><mn>135</mn><mo>,</mo><mn>137</mn><mo>,</mo><mn>139</mn></mrow></mmultiscripts></math> isotopes. This is the first lifetime data on iodine isotopes beyond <math><mrow><mi>N</mi><mo>=</mo><mn>82</mn></mrow></math>. Excited states were populated in fast neutron-induced fission of <math><mmultiscripts><mi mathvariant="normal">U</mi><mprescripts/><none/><mn>238</mn></mmultiscripts></math> at the ALTO facility of IJCLab with the LICORNE neutron source and detected using the hybrid <math><mi>ν</mi></math>-ball spectrometer. The level schemes of the <math><mmultiscripts><mi mathvariant="normal">I</mi><mprescripts/><none/><mrow><mn>135</mn><mo>,</mo><mn>137</mn><mo>,</mo><mn>139</mn></mrow></mmultiscripts></math> isotopes are revised in terms of excited states with up to maximum spin-parity of <math><mrow><mo>(</mo><mn>33</mn><mo>/</mo><msup><mn>2</mn><mo>+</mo></msup><mo>)</mo></mrow></math>, populated for the first time in fast neutron-induced fission. We provide first results on the lifetimes of the <math><mrow><mo>(</mo><mn>9</mn><mo>/</mo><msubsup><mn>2</mn><mn>1</mn><mo>+</mo></msubsup><mo>)</mo></mrow></math> and <math><mrow><mo>(</mo><mn>13</mn><mo>/</mo><msubsup><mn>2</mn><mn>1</mn><mo>+</mo></msubsup><mo>)</mo></mrow></math> states in <math><mmultiscripts><mi mathvariant="normal">I</mi><mprescripts/><none/><mn>137</mn></mmultiscripts></math> and <math><mmultiscripts><mi mathvariant="normal">I</mi><mprescripts/><none/><mn>139</mn></mmultiscripts></math>, and the <math><mrow><mo>(</mo><mn>17</mn><mo>/</mo><msubsup><mn>2</mn><mn>1</mn><mo>+</mo></msubsup><mo>)</mo></mrow></math> state in <math><mmultiscripts><mi mathvariant="normal">I</mi><mprescripts/><none/><mn>137</mn></mmultiscripts></math>. In addition, we give upper lifetime limits for the <math><mrow><mo>(</mo><mn>11</mn><mo>/</mo><msubsup><mn>2</mn><mn>1</mn><mo>+</mo></msubsup><mo>)</mo></mrow></math> states in <math><mmultiscripts><mi mathvariant="normal">I</mi><mprescripts/><none/><mrow><mn>135</mn><mo>−</mo><mn>139</mn></mrow></mmultiscripts></math>, the <math><mrow><mo>(</mo><mn>15</mn><mo>/</mo><msubsup><mn>2</mn><mn>1</mn><mo>+</mo></msubsup><mo>)</mo></mrow></math> state in <math><mmultiscripts><mi mathvariant="normal">I</mi><mprescripts/><none/><mn>137</mn></mmultiscripts></math>, the <math><mrow><mo>(</mo><mn>17</mn><mo>/</mo><msubsup><mn>2</mn><mn>1</mn><mo>+</mo></msubsup><mo>)</mo></mrow></math> state in <math><mmultiscripts><mi mathvariant="normal">I</mi><mprescripts/><none/><mn>139</mn></mmultiscripts></math>, and reexamine the <math><mrow><mo>(</mo><mn>29</mn><mo>/</mo><msubsup><mn>2</mn><mn>1</mn><mo>+</mo></msubsup><mo>)</mo></mrow></math> state in <math><mmultiscripts><mi mathvariant="normal">I</mi><mprescripts/><none/><mn>137</mn></mmultiscripts></math>. The isomeric data in <math><mmultiscripts><mi mathvariant="normal">I</mi><mprescripts/><none/><mn>135</mn></mmultiscripts></math> are reinvestigated, such as the previously known <math><mrow><mo>(</mo><mn>15</mn><mo>/</mo><msubsup><mn>2</mn><mn>1</mn><mo>+</mo></msubsup><mo>)</mo></mrow></math> and <math><mrow><mo>(</mo><mn>23</mn><mo>/</mo><msubsup><mn>2</mn><mn>1</mn><mo>−</mo></msubsup><mo>)</mo></mrow></math> isomers with <math><msub><mi>T</mi><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msub></math> of 1.64(14) and 4.6(7) ns, respectively, as obtained in this work. The new spectroscopic information is compared to that from spontaneous or thermal-neutron induced fission and discussed in the context of large scale shell-model (LSSM) calculations for the region beyond <math><mmultiscripts><mi>Sn</mi><mprescripts/><none/><mn>132</mn></mmultiscripts></math>, indicating the behavior of collectivity for the three valence-proton iodine chain with <math><mrow><mi>N</mi><mo>=</mo><mn>82</mn><mo>,</mo><mn>84</mn><mo>,</mo><mn>86</mn></mrow></math>.Read less <