A Danilov-type formula for toric origami manifolds via localization of index

Abstract

We give a direct geometric proof of a Danilov-type formula for toric origami manifolds by using the localization of Riemann-Roch number.

30 pages, 8 figures : Revision of the introduction. Added references : Typos corrected. Construction in Section 4.1 simplified. Proofs of Lemma 6.2 and Theorem 6.12 corrected. Acknowledgement for the referee added : Final version, to appear in Osaka Journal of Mathematics

References in corpus (4)

• Applications of Equivariant Cohomology
• Toric origami manifolds and multi-fans
• $S^1$-equivariant local index and transverse index for non-compact symplectic manifolds
• The equivariant local index of the reduced space in the symplectic cutting