diff --git a/kadison_kaplansky_projection_counter_v2.txt b/kadison_kaplansky_projection_counter_v2.txt
index f37fecf..ff43de1 100644
--- a/kadison_kaplansky_projection_counter_v2.txt
+++ b/kadison_kaplansky_projection_counter_v2.txt
@@ -212,7 +212,7 @@ which is a homomorphism from a "topological" (geometry of the
 group) K-theory to the operator K-theory.  A theorem of Lueck
 (Inventiones 149 (2002), 123-152), extended
 by Baum-Guentner-Willett (see the local survey
-bgw-2016-exactness-kadison-kaplansky.pdf), says: for a
+./pdf/bgw-2016-exactness-kadison-kaplansky.pdf), says: for a
 torsion-free group, the canonical trace tau is integral on the
 IMAGE of the reduced assembly map.  So:
 
@@ -1848,7 +1848,7 @@ ONE incidence at x of type v.
 
 Consequence: the equivariant vertex space
 
-   oplus over Q of  l^2(V(Q))
+   ⊕ over Q of  l^2(V(Q))
 
 is canonically identified with
 
@@ -2383,9 +2383,9 @@ In particular F_Q != 0 whenever E_Q != 0.
 
 Form the orthogonal direct sums
 
-   C     =  oplus_Q C_Q     + 0  on unassigned vertices,
-   T_D   =  oplus_Q T_Q|_{D_Q} + 0  on unassigned vertices,
-   F_D   =  oplus_Q F_Q     + 0  on unassigned vertices.
+   C     =  ⊕_Q C_Q     + 0  on unassigned vertices,
+   T_D   =  ⊕_Q T_Q|_{D_Q} + 0  on unassigned vertices,
+   F_D   =  ⊕_Q F_Q     + 0  on unassigned vertices.
 
 The assigned domains D_Q are disjoint, so both C and T_D are
 bounded operators on l^2(Gamma) (x) C^N.  From 10.6,
@@ -2462,7 +2462,7 @@ most ||T - C|| away from the spectrum of C.  So
    spectrum(T)  contained in
       (-infinity, 1 - chi + 4 alpha]  UNION  [1 - 3 alpha, 1 + 3 alpha].
 
-NONVANISHING.  Since F_D = oplus_Q F_Q and each F_Q != 0 by the trimming estimate,
+NONVANISHING.  Since F_D = ⊕_Q F_Q and each F_Q != 0 by the trimming estimate,
 the upper interval [1 - 3 alpha, 1 + 3 alpha] is nonempty.
 
 GAP.  The number 1 - chi/4 lies strictly between the two
@@ -2488,11 +2488,11 @@ p_0 from above.
 Use ALL the indexed copies at once.  The equivariant vertex
 space is
 
-   L  =  oplus_Q l^2(V(Q)) (x) C^N
+   L  =  ⊕_Q l^2(V(Q)) (x) C^N
       =  l^2(Gamma)  (x)  l^2(V(Y))  (x) C^N  =  H (x) l^2(V(Y))
    (incidence identification).
 
-Let E = oplus_Q E_Q.  Its identity trace is
+Let E = ⊕_Q E_Q.  Its identity trace is
 
    Tr_L(E)  =  S_0  =  sum over surviving base vertices v of e_v
                     <=  S  <  infinity.
@@ -2686,7 +2686,7 @@ The theorem is proved.
 K_0(C_r*(Gamma)) has trace tau_{Gamma,N}(p_0) in (0, 1/2), which
 is not an integer.  Lueck (Inventiones 149 (2002), 123-152) and
 Baum-Guentner-Willett (local file
-bgw-2016-exactness-kadison-kaplansky.pdf) prove that the reduced
+./pdf/bgw-2016-exactness-kadison-kaplansky.pdf) prove that the reduced
 assembly map with trivial coefficients lands in the integral
 part of K_0-trace for torsion-free groups.