$$G$$-monopole classes, Ricci flow, and Yamabe invariants of 4-manifolds

Content Provider	Semantic Scholar
Author	Sung, Chanyoung
Copyright Year	2012
Abstract	On a smooth closed oriented 4-manifold $$M$$ with a smooth action by a finite group $$G$$, we show that a $$G$$-monopole class gives the $$L^2$$-estimate of the Ricci curvature of a $$G$$-invariant Riemannian metric, and derive a topological obstruction to the existence of a $$G$$-invariant nonsingular solution to the normalized Ricci flow on $$M$$. In particular, for certain $$m$$ and $$n, m\mathbb C P_2 \# n\overline{\mathbb{C P}}_2$$ admits an infinite family of topologically equivalent but smoothly distinct non-free actions of $$\mathbb Z _d$$ such that it admits no nonsingular solution to the normalized Ricci flow for any initial metric invariant under such an action, where $$d>1$$ is a non-prime integer. We also compute the $$G$$-Yamabe invariants of some 4-manifolds with $$G$$-monopole classes and the orbifold Yamabe invariants of some 4-orbifolds.
Starting Page	129
Ending Page	144
Page Count	16
File Format	PDF HTM / HTML
DOI	10.1007/s10711-013-9846-1
Alternate Webpage(s)	https://arxiv.org/pdf/1205.3871v2.pdf
Alternate Webpage(s)	https://doi.org/10.1007/s10711-013-9846-1
Volume Number	169
Language	English
Access Restriction	Open
Content Type	Text
Resource Type	Article