## The fixed-point construction in equivariant bordism

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- by Russell J. Rowlett PDF
- Trans. Amer. Math. Soc.
**246**(1978), 473-481 Request permission

## Abstract:

Consider the bordism ${\Omega _ {\ast }}(G)$ of smooth*G*-actions. If

*K*is a subgroup of

*G*, with normalizer

*NK*, there is a standard $NK/K$-action on ${\Omega _ {\ast }}(K)$(All, Proper). If

*M*has a smooth

*G*-action, a tubular neighborhood of the fixed set of

*K*in

*M*represents an element of ${\Omega _ {\ast }}(K){({\text {All, Proper}})^{NK/K}}$. One thus obtains the “fixed point homomorphism” $\phi$ carrying ${\Omega _ {\ast }}(G)$ to the sum of the ${\Omega _ {\ast }}(K){({\text {All, Proper}})^{NK/K}}$, summed over conjugacy classes of subgroups

*K*. Let

*P*be the collection of primes not dividing the order of

*G*. We show that the

*P*-localization of $\phi$ is an isomorphism, and give several applications.

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## Additional Information

- © Copyright 1978 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**246**(1978), 473-481 - MSC: Primary 57R85
- DOI: https://doi.org/10.1090/S0002-9947-1978-0515553-5
- MathSciNet review: 515553