Abstract
Let $M$ be an even-dimensional closed oriented manifold and $g$ a periodic automorphism of $M$ of order $p$. In this paper, under the assumption that the fixed points of $g^k\;(1\leq k\leq p-1)$ are isolated, a calculation formula is provided for the homomorphism $I_D:{\Bbb Z}_p\to{\Bbb R}/{\Bbb Z}$ defined in [6] for equivariant twisted signature operators $D$ over $M$. The formula gives a new method to study the periodic automorphisms of oriented manifolds. As examples of the application of the formula, results about the existence of the cyclic group action for 2,4,6-dimensional closed oriented manifolds are obtained.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
