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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Wall manifolds with involution
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by R. J. Rowlett PDF
Trans. Amer. Math. Soc. 169 (1972), 153-162 Request permission


Consider smooth manifolds $W$ with involution $t$ and a Wall structure described by a map $f:W \to {S^1}$ such that $ft = f$. For such objects we define cobordism theories ${\text {W}}_\ast ^I$ (in case $W$ is closed, $t$ unrestricted), ${\text {W}}_ \ast ^F$ (for $W$ closed, $t$ fixed-point free), and ${\text {W}}_ \ast ^{{\text {rel}}}$ ($W$ with boundary, $t$ free on $W$). We prove that there is an exact sequence \[ 0 \to {\text {W}}_ \ast ^I \to {\text {W}}_ \ast ^{{\text {rel}}} \to {\text {W}}_ \ast ^F \to 0.\] As a corollary, ${\text {W}}_ \ast ^I$ imbeds in the cobordism of unoriented manifolds with involution. We also describe how ${\text {W}}_ \ast ^I$ determines the $2$-torsion in the cobordism of oriented manifolds with involution.
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Additional Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 169 (1972), 153-162
  • MSC: Primary 57D75
  • DOI:
  • MathSciNet review: 0314076