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Can we define Lefschetz number using cohomology with integer coefficient?
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Lefschetz number equal to Euler Characteristic of Fixed PointsThe Lefschetz Fixed Point Theorem in Coefficient Ring $G$Number of Fixed Points in a Map from the Torus to itself using Lefschetz TracePoincare-Lefschetz duality, universal coefficients, and middle cohomologyProve that for a path connected topological group $G$ the Euler characteristic $chi (G)$ is zero.Lefschetz number and Euler characteristicLefschetz number of $fcolon Bbb R P^1to Bbb R P^1$Coincidence of different definitions of Lefschetz numberLefschetz fixed point theorem induced map on homology of $RP^n$Lefschetz number of constant map
$begingroup$
Consider a map $ f: X to X$ of a finite CW-complex $X$. My question is it correct to define Lefschetz number $L(f)$ as the following
$$ L(f)= sum_n tr (f^*: H^n(X;Bbb Z) to H^n(X;Bbb Z))?$$
Here $tr(f^*)$ is the trace of the induced homomorphism $overline f^*: H^n(X;Bbb Z)/textrmTorsionto H^n(X;Bbb Z)/textrmTorsion$.
algebraic-topology
asked Mar 25 at 8:08
mathstudentmathstudent
394
$endgroup$
add a comment |
$begingroup$
Consider a map $ f: X to X$ of a finite CW-complex $X$. My question is it correct to define Lefschetz number $L(f)$ as the following
$$ L(f)= sum_n tr (f^*: H^n(X;Bbb Z) to H^n(X;Bbb Z))?$$
Here $tr(f^*)$ is the trace of the induced homomorphism $overline f^*: H^n(X;Bbb Z)/textrmTorsionto H^n(X;Bbb Z)/textrmTorsion$.
algebraic-topology
asked Mar 25 at 8:08
mathstudentmathstudent
394
$endgroup$
$begingroup$
Yes, it's the same as the trace over the rationals.
$endgroup$
– Qiaochu Yuan
Mar 26 at 6:21
add a comment |
$begingroup$
Consider a map $ f: X to X$ of a finite CW-complex $X$. My question is it correct to define Lefschetz number $L(f)$ as the following
$$ L(f)= sum_n tr (f^*: H^n(X;Bbb Z) to H^n(X;Bbb Z))?$$
Here $tr(f^*)$ is the trace of the induced homomorphism $overline f^*: H^n(X;Bbb Z)/textrmTorsionto H^n(X;Bbb Z)/textrmTorsion$.
algebraic-topology
asked Mar 25 at 8:08
mathstudentmathstudent
394
$endgroup$
Consider a map $ f: X to X$ of a finite CW-complex $X$. My question is it correct to define Lefschetz number $L(f)$ as the following
$$ L(f)= sum_n tr (f^*: H^n(X;Bbb Z) to H^n(X;Bbb Z))?$$
Here $tr(f^*)$ is the trace of the induced homomorphism $overline f^*: H^n(X;Bbb Z)/textrmTorsionto H^n(X;Bbb Z)/textrmTorsion$.
algebraic-topology
algebraic-topology
asked Mar 25 at 8:08
mathstudentmathstudent
394
asked Mar 25 at 8:08
mathstudentmathstudent
394
edited Mar 26 at 6:05
mathstudent
asked Mar 25 at 8:08
mathstudentmathstudent
394
asked Mar 25 at 8:08
mathstudentmathstudent
394
asked Mar 25 at 8:08
mathstudentmathstudent
394
394
$begingroup$
Yes, it's the same as the trace over the rationals.
$endgroup$
– Qiaochu Yuan
Mar 26 at 6:21
add a comment |
$begingroup$
Yes, it's the same as the trace over the rationals.
$endgroup$
– Qiaochu Yuan
Mar 26 at 6:21
$begingroup$
Yes, it's the same as the trace over the rationals.
$endgroup$
– Qiaochu Yuan
Mar 26 at 6:21
$begingroup$
Yes, it's the same as the trace over the rationals.
$endgroup$
– Qiaochu Yuan
Mar 26 at 6:21
add a comment |
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$begingroup$
Yes, it's the same as the trace over the rationals.
$endgroup$
– Qiaochu Yuan
Mar 26 at 6:21