Chern character of wedge bundle
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Given a vector bundle $E$, let's consider the direct sum of wedge bundle of $E$: $bigoplus_i bigwedge ^iE$, let's call this $cal E$. Given a connection $nabla $ on $E$, its Chern character is given by $operatorname{tr}left(expdfrac{inabla ^2}{2pi}right)$.
My question is what will be the Chern character of $cal E$? Is it given by $detleft(1-expdfrac{inabla ^2}{2pi}right)$?
differential-geometry complex-geometry
edited yesterday
user10354138
6,199523
asked yesterday
user330928
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Given a vector bundle $E$, let's consider the direct sum of wedge bundle of $E$: $bigoplus_i bigwedge ^iE$, let's call this $cal E$. Given a connection $nabla $ on $E$, its Chern character is given by $operatorname{tr}left(expdfrac{inabla ^2}{2pi}right)$.
My question is what will be the Chern character of $cal E$? Is it given by $detleft(1-expdfrac{inabla ^2}{2pi}right)$?
differential-geometry complex-geometry
edited yesterday
user10354138
6,199523
asked yesterday
user330928
35227
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Given a vector bundle $E$, let's consider the direct sum of wedge bundle of $E$: $bigoplus_i bigwedge ^iE$, let's call this $cal E$. Given a connection $nabla $ on $E$, its Chern character is given by $operatorname{tr}left(expdfrac{inabla ^2}{2pi}right)$.
My question is what will be the Chern character of $cal E$? Is it given by $detleft(1-expdfrac{inabla ^2}{2pi}right)$?
differential-geometry complex-geometry
edited yesterday
user10354138
6,199523
asked yesterday
user330928
35227
Given a vector bundle $E$, let's consider the direct sum of wedge bundle of $E$: $bigoplus_i bigwedge ^iE$, let's call this $cal E$. Given a connection $nabla $ on $E$, its Chern character is given by $operatorname{tr}left(expdfrac{inabla ^2}{2pi}right)$.
My question is what will be the Chern character of $cal E$? Is it given by $detleft(1-expdfrac{inabla ^2}{2pi}right)$?
differential-geometry complex-geometry
differential-geometry complex-geometry
edited yesterday
user10354138
6,199523
asked yesterday
user330928
35227
edited yesterday
user10354138
6,199523
asked yesterday
user330928
35227
edited yesterday
user10354138
6,199523
edited yesterday
user10354138
6,199523
edited yesterday
user10354138
6,199523
6,199523
asked yesterday
user330928
35227
asked yesterday
user330928
35227
asked yesterday
user330928
35227
35227
add a comment |
add a comment |
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