diff --git a/gtsam/base/LieMatrix.h b/gtsam/base/LieMatrix.h
index 7c167a46b..90b7207a2 100644
--- a/gtsam/base/LieMatrix.h
+++ b/gtsam/base/LieMatrix.h
@@ -31,7 +31,7 @@
 namespace gtsam {
 
 /**
- * @deprecated: LieScalar, LieVector and LieMatrix are obsolete in GTSAM 4.0 as
+ * @deprecated: LieMatrix, LieVector and LieMatrix are obsolete in GTSAM 4.0 as
  * we can directly add double, Vector, and Matrix into values now, because of
  * gtsam::traits.
  */
@@ -83,6 +83,26 @@ struct LieMatrix : public Matrix {
   }
 
   /// @}
+
+  /// @name Group
+  /// @{
+  LieMatrix compose(const LieMatrix& q) { return (*this)+q;}
+  LieMatrix between(const LieMatrix& q) { return q-(*this);}
+  LieMatrix inverse() { return -(*this);}
+  /// @}
+
+  /// @name Manifold
+  /// @{
+  Vector localCoordinates(const LieMatrix& q) { return between(q).vector();}
+  LieMatrix retract(const Vector& v) {return compose(LieMatrix(v));}
+  /// @}
+
+  /// @name Lie Group
+  /// @{
+  static Vector Logmap(const LieMatrix& p) {return p.vector();}
+  static LieMatrix Expmap(const Vector& v) { return LieMatrix(v);}
+  /// @}
+
   /// @name VectorSpace requirements
   /// @{
 
diff --git a/gtsam/base/LieScalar.h b/gtsam/base/LieScalar.h
index 2e4be834f..9f6c56b28 100644
--- a/gtsam/base/LieScalar.h
+++ b/gtsam/base/LieScalar.h
@@ -49,17 +49,36 @@ namespace gtsam {
     /** Automatic conversion to underlying value */
     operator double() const { return d_; }
 
+    /** convert vector */
+    Vector1 vector() const { Vector1 v; v<<d_; return v; }
+
     /// @name Testable
     /// @{
-
-    /** print @param name optional string naming the object */
     void print(const std::string& name="") const;
-
-    /** equality up to tolerance */
     bool equals(const LieScalar& expected, double tol=1e-5) const {
       return fabs(expected.d_ - d_) <= tol;
     }
+    /// @}
 
+    /// @name Group
+    /// @{
+    static LieScalar identity() { return LieScalar(0);}
+    LieScalar compose(const LieScalar& q) { return (*this)+q;}
+    LieScalar between(const LieScalar& q) { return q-(*this);}
+    LieScalar inverse() { return -(*this);}
+    /// @}
+
+    /// @name Manifold
+    /// @{
+    size_t dim() const { return 1; }
+    Vector1 localCoordinates(const LieScalar& q) { return between(q).vector();}
+    LieScalar retract(const Vector1& v) {return compose(LieScalar(v[0]));}
+    /// @}
+
+    /// @name Lie Group
+    /// @{
+    static Vector1 Logmap(const LieScalar& p) { return p.vector();}
+    static LieScalar Expmap(const Vector1& v) { return LieScalar(v[0]);}
     /// @}
 
   private:
diff --git a/gtsam/base/LieVector.h b/gtsam/base/LieVector.h
index 360c376ec..c2003df3c 100644
--- a/gtsam/base/LieVector.h
+++ b/gtsam/base/LieVector.h
@@ -28,7 +28,7 @@
 namespace gtsam {
 
 /**
- * @deprecated: LieScalar, LieVector and LieMatrix are obsolete in GTSAM 4.0 as
+ * @deprecated: LieVector, LieVector and LieMatrix are obsolete in GTSAM 4.0 as
  * we can directly add double, Vector, and Matrix into values now, because of
  * gtsam::traits.
  */
@@ -60,16 +60,31 @@ struct LieVector : public Vector {
 
   /// @name Testable
   /// @{
-
-  /** print @param name optional string naming the object */
   GTSAM_EXPORT void print(const std::string& name="") const;
-
-  /** equality up to tolerance */
   bool equals(const LieVector& expected, double tol=1e-5) const {
     return gtsam::equal(vector(), expected.vector(), tol);
   }
-
   /// @}
+
+  /// @name Group
+  /// @{
+  LieVector compose(const LieVector& q) { return (*this)+q;}
+  LieVector between(const LieVector& q) { return q-(*this);}
+  LieVector inverse() { return -(*this);}
+  /// @}
+
+  /// @name Manifold
+  /// @{
+  Vector localCoordinates(const LieVector& q) { return between(q).vector();}
+  LieVector retract(const Vector& v) {return compose(LieVector(v));}
+  /// @}
+
+  /// @name Lie Group
+  /// @{
+  static Vector Logmap(const LieVector& p) {return p.vector();}
+  static LieVector Expmap(const Vector& v) { return LieVector(v);}
+  /// @}
+
   /// @name VectorSpace requirements
   /// @{
 
diff --git a/gtsam/geometry/Point2.h b/gtsam/geometry/Point2.h
index 0a2735861..01a6d6052 100644
--- a/gtsam/geometry/Point2.h
+++ b/gtsam/geometry/Point2.h
@@ -160,10 +160,18 @@ public:
   Vector2 vector() const { return Vector2(x_, y_); }
 
   /// @}
-  /// @name Deprecated (non-const, non-functional style. Do not use).
+
+  /// @name Deprecated
   /// @{
   inline void operator += (const Point2& q) {x_+=q.x_;y_+=q.y_;}
   inline void operator *= (double s) {x_*=s;y_*=s;}
+  Point2 inverse() { return -(*this);}
+  Point2 compose(const Point2& q) { return (*this)+q;}
+  Point2 between(const Point2& q) { return q-(*this);}
+  Vector2 localCoordinates(const Point2& q) { return between(q).vector();}
+  Point2 retract(const Vector2& v) {return compose(Point2(v));}
+  static Vector2 Logmap(const Point2& p) {return p.vector();}
+  static Point2 Expmap(const Vector2& v) { return Point2(v);}
   /// @}
 
   /// Streaming
diff --git a/gtsam/geometry/Point3.h b/gtsam/geometry/Point3.h
index 468a08c33..5b133dc60 100644
--- a/gtsam/geometry/Point3.h
+++ b/gtsam/geometry/Point3.h
@@ -162,6 +162,17 @@ namespace gtsam {
     /// Output stream operator
     GTSAM_EXPORT friend std::ostream &operator<<(std::ostream &os, const Point3& p);
 
+    /// @name Deprecated
+    /// @{
+    Point3 inverse() { return -(*this);}
+    Point3 compose(const Point3& q) { return (*this)+q;}
+    Point3 between(const Point3& q) { return q-(*this);}
+    Vector3 localCoordinates(const Point3& q) { return between(q).vector();}
+    Point3 retract(const Vector3& v) {return compose(Point3(v));}
+    static Vector3 Logmap(const Point3& p) {return p.vector();}
+    static Point3 Expmap(const Vector3& v) { return Point3(v);}
+    /// @}
+
   private:
 
     /// @name Advanced Interface
diff --git a/gtsam/navigation/ImuBias.h b/gtsam/navigation/ImuBias.h
index da01af613..ce93bd740 100644
--- a/gtsam/navigation/ImuBias.h
+++ b/gtsam/navigation/ImuBias.h
@@ -159,6 +159,17 @@ namespace imuBias {
 
     /// @}
 
+    /// @name Deprecated
+    /// @{
+    ConstantBias inverse() { return -(*this);}
+    ConstantBias compose(const ConstantBias& q) { return (*this)+q;}
+    ConstantBias between(const ConstantBias& q) { return q-(*this);}
+    Vector6 localCoordinates(const ConstantBias& q) { return between(q).vector();}
+    ConstantBias retract(const Vector6& v) {return compose(ConstantBias(v));}
+    static Vector6 Logmap(const ConstantBias& p) {return p.vector();}
+    static ConstantBias Expmap(const Vector6& v) { return ConstantBias(v);}
+    /// @}
+
   private:
 
     /// @name Advanced Interface