OAI/Topology/CoarseAssembly/MultiplierUnitaryHomotopy.lean

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6 declarations, 0 contain sorry, 0 declared as axioms

Unitary homotopies preserve the Roe multiplier boundary

This is the conjugation step in descent through changes of cycle coordinates. The path is an actual norm-continuous path of unitaries in the Roe multiplier algebra.

  1. def OAI.CoarseAssembly.DiscreteRoe.conjugatedMultiplier line 22
  2. theorem OAI.CoarseAssembly.DiscreteRoe.conjugatedMultiplier_selfAdjoint line 26
  3. theorem OAI.CoarseAssembly.DiscreteRoe.conjugatedMultiplier_square_defect line 34
  4. theorem OAI.CoarseAssembly.DiscreteRoe.conjugatedMultiplier_defect_mem line 48
  5. theorem OAI.CoarseAssembly.DiscreteRoe.multiplierBoundaryClass_unitaryHomotopy line 63
  6. theorem OAI.CoarseAssembly.DiscreteRoe.multiplierBoundaryClass_involutionConjugation line 80