ncg

commit f4c253f98f2b65a21125c0aeb306bce96475dcdc
parent fe3576e04e90396a6455ff69235e8e5cdf40b125
Author: miksa234 <milutin@popovic.xyz>
Date:   Sun, 16 May 2021 18:46:56 +0200

small fix

Diffstat:
M
pdfs/week8.pdf
 | 
0

M
src/week8.tex
 | 
10
+++++-----

2 files changed, 5 insertions(+), 5 deletions(-)
diff --git a/pdfs/week8.pdf b/pdfs/week8.pdf
Binary files differ.
diff --git a/src/week8.tex b/src/week8.tex
@@ -523,9 +523,9 @@ where $J_F$ and $\gamma_F$ like before, $D_F$ like above.
 The almost commutative manifold $M\times F_{ED}$ has KO-dim$=2$, it is the
 following spectral triple
 \begin{align}
-    M\times F_{ED} := \left(C^\infty(M,\mathbb{C}^2, L^2(S)\otimes
-    \mathbb{C}^4,
-    D_M\otimes 1 +\gamma _M \otimes D_F; J_M\otimes J_F, \gamma_M\otimes
+    M\times F_{ED} := \left(C^\infty(M,\mathbb{C}^2),\ L^2(S)\otimes
+    \mathbb{C}^4,\
+    D_M\otimes 1 +\gamma _M \otimes D_F;\; J_M\otimes J_F,\ \gamma_M\otimes
     \gamma _F\right)
 \end{align}
 
@@ -561,8 +561,8 @@ gauge group
 \end{align}
 
 Our space $N = M\times X \simeq M\sqcup M$ consists of two compies of $M$.
-If $D_F = 0$ we have infinite distance of the two copies. Now we have $D_F$
-nonzero but the $[D_F, a] = 0$ $\forall a \in A$ which still yields infinite
+If $D_F = 0$ we have infinite distance between the two copies. Now we have $D_F$
+nonzero but $[D_F, a] = 0$ $\forall a \in A$ which still yields infinite
 distance.
 \begin{question}
     What does this imply (physically, mathematically)? Why can we continue