Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



The fixed-point construction in equivariant bordism

Author: Russell J. Rowlett
Journal: Trans. Amer. Math. Soc. 246 (1978), 473-481
MSC: Primary 57R85
MathSciNet review: 515553
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 57R85

Retrieve articles in all journals with MSC: 57R85

Additional Information

Keywords: Finite group actions, equivalent bordism, fixed point homomorphism
Article copyright: © Copyright 1978 American Mathematical Society

American Mathematical Society