OAI/GroupTheory/PolycyclicRecognition/Finiteness/LocallyFiniteCoefficientHomology.lean

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6 declarations, 0 contain sorry, 0 declared as axioms

Uniform rational bounds through locally finite kernels

The comparison holds for arbitrary coefficient representations and therefore transports a uniform homology bound in both directions. For nilpotent groups it relates finite rational rank to the torsion-free quotient's dimension.

  1. def OAI.PolycyclicRecognition.locallyFiniteKernelCoefficientHomologyIso line 18
  2. def OAI.PolycyclicRecognition.locallyFiniteKernelInflationHomologyIso line 25
  3. theorem OAI.PolycyclicRecognition.locallyFiniteKernel_rational_homology_bound_iff line 33
  4. theorem OAI.PolycyclicRecognition.rational_homology_bound_of_integral_dimension line 45
  5. theorem OAI.PolycyclicRecognition.rational_homology_bound_of_finiteIndex_dimension line 51
  6. theorem OAI.PolycyclicRecognition.nilpotent_rational_homology_bounded_iff_torsionQuotient_finiteDimension line 59