Revert BUG: Ensure same index is returned for slow and fast path in …

doc/source/whatsnew/v1.1.0.rst

@@ -1114,10 +1114,6 @@ Groupby/resample/rolling
 - Bug in :meth:`DataFrame.resample` where an ``AmbiguousTimeError`` would be raised when the resulting timezone aware :class:`DatetimeIndex` had a DST transition at midnight (:issue:`25758`)
 - Bug in :meth:`DataFrame.groupby` where a ``ValueError`` would be raised when grouping by a categorical column with read-only categories and ``sort=False`` (:issue:`33410`)
 - Bug in :meth:`GroupBy.agg`, :meth:`GroupBy.transform`, and :meth:`GroupBy.resample` where subclasses are not preserved (:issue:`28330`)
-- Bug in :meth:`core.groupby.DataFrameGroupBy.apply` where the output index shape for functions returning a DataFrame which is equally indexed
-  to the input DataFrame is inconsistent. An internal heuristic to detect index mutation would behave differently for equal but not identical
-  indices. In particular, the result index shape might change if a copy of the input would be returned.
-  The behaviour now is consistent, independent of internal heuristics. (:issue:`31612`, :issue:`14927`, :issue:`13056`)
 - Bug in :meth:`SeriesGroupBy.agg` where any column name was accepted in the named aggregation of ``SeriesGroupBy`` previously. The behaviour now allows only ``str`` and callables else would raise ``TypeError``. (:issue:`34422`)
 - Bug in :meth:`DataFrame.groupby` lost index, when one of the ``agg`` keys referenced an empty list (:issue:`32580`)
 - Bug in :meth:`Rolling.apply` where ``center=True`` was ignored when ``engine='numba'`` was specified (:issue:`34784`)

pandas/_libs/reduction.pyx

@@ -366,7 +366,7 @@ def apply_frame_axis0(object frame, object f, object names,
             # Need to infer if low level index slider will cause segfaults
             require_slow_apply = i == 0 and piece is chunk
             try:
-                if not piece.index.equals(chunk.index):
+                if not piece.index is chunk.index:
                     mutated = True
             except AttributeError:
                 # `piece` might not have an index, could be e.g. an int

pandas/tests/groupby/test_apply.py

@@ -211,6 +211,7 @@ def test_group_apply_once_per_group2(capsys):
     assert result == expected
 
 
+@pytest.mark.xfail(reason="GH-34998")
 def test_apply_fast_slow_identical():
     # GH 31613
 
@@ -234,9 +235,11 @@ def fast(group):
     "func",
     [
         lambda x: x,
-        lambda x: x[:],
+        pytest.param(lambda x: x[:], marks=pytest.mark.xfail(reason="GH-34998")),
         lambda x: x.copy(deep=False),
-        lambda x: x.copy(deep=True),
+        pytest.param(
+            lambda x: x.copy(deep=True), marks=pytest.mark.xfail(reason="GH-34998")
+        ),
     ],
 )
 def test_groupby_apply_identity_maybecopy_index_identical(func):
@@ -997,6 +1000,7 @@ def test_apply_function_with_indexing_return_column():
     tm.assert_frame_equal(result, expected)
 
 
+@pytest.mark.xfail(reason="GH-34998")
 def test_apply_with_timezones_aware():
     # GH: 27212