Upper bounds for virtual dimensions of Seiberg-Witten moduli spaces

Abstract

Given a closed four-manifold with $b_1=0$ and a prime number $p$, we prove that for any mod $p^r$ basic class, the virtual dimension of the Seiberg-Witten moduli space is bounded above by $2r(p-1)-2$ under some conditions on $r$ and $b_2^{+}$. As an application, we obtain adjunction inequalities for embedded surfaces with negative self-intersection number.

20 pages. Main results improved

References in corpus (1)

• Stable Cohomotopy Seiberg-Witten Invariants of Connected Sums of Four-Manifolds with Positive First Betti Number