OAI/Topology/CoarseAssembly/RawCycleIndex.lean

GitHub source file

6 declarations, 0 contain sorry, 0 declared as axioms

A Fredholm index defined on every odd cycle

The operator uses the explicit self-adjoint cut-down and varies continuously along any Fredholm-module homotopy. Its definition makes no spectral choices.

  1. def OAI.CoarseAssembly.Analytic.rawCycleToeplitz line 19
  2. def OAI.CoarseAssembly.Analytic.rawCycleIndex line 24
  3. theorem OAI.CoarseAssembly.Analytic.rawCycleToeplitz_compact_defects line 26
  4. theorem OAI.CoarseAssembly.Analytic.rawCycleToeplitz_fredholm line 59
  5. theorem OAI.CoarseAssembly.Analytic.rawCycleIndex_homotopy line 64
  6. theorem OAI.CoarseAssembly.Analytic.rawCycleIndex_precomp line 88