TY - JOUR
AU - Miller, Edward Y.
AB - A FORMULA FOR THE BROWDER-LIVESAY INVARIANT OF AN INVOLUTION BENJAMIN M. MANN AND EDWAR D Y. MILLER Introduction 2k l Let (M ~ , T) be a closed, compact, 2k — 1 dimensional PL manifold with a free 2k orientation preserving involution T. When k is even and (M ~\ T) equivariantly 2k bounds a compact 2k manifold (Y , T), Hirzebruch and Janich [5] have given a 2k l formula which expresses the Browder-Livesay invariant of {M ~ ,T) totally in 2k terms of {Y , T). In this paper we prove an analogous theorem for the case when k is odd under 2k the additional hypotheses that T is free on all of Y and that a certain characteristic 2 1 class, 9 {M,T) in /^(M *" , Z/2), vanishes. (These classes d and their k k generalizations are studied in detail in [3].) As our proof is completely homological an extension of this theorem remains true in the category of Z/2-Poincare duality spaces. Thus we also obtain a result closely related to some recent work of Hambleton and Milgram [4] on the obstruction to the existence of Poincare duality characteristic varieties. In Section 1 we recall 
TI - A Formula for the Browder‐Livesay Invariant of an Involution
JO - Journal of the London Mathematical Society
DO - 10.1112/jlms/s2-24.2.335
DA - 1981-10-01
UR - https://www.deepdyve.com/lp/wiley/a-formula-for-the-browder-livesay-invariant-of-an-involution-Ejj406bAzB
SP - 335
EP - 345
VL - s2-24
IS - 2
DP - DeepDyve
ER -