New Bochner type theorems

Article Mathematics, Applied

A RIGIDITY THEOREM FOR KILLING VECTOR FIELDS ON COMPACT MANIFOLDS WITH ALMOST NONPOSITIVE RICCI CURVATURE

Atsushi Katsuda et al.

Summary: This study proves a rigidity theorem for Killing vector fields on manifolds with almost nonpositive Ricci curvature, which is a generalization of Bochner's classical results.

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY (2021)

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Article Mathematics

CONSISTENCY OF M-THEORY ON NON-ORIENTABLE MANIFOLDS

Daniel S. Freed et al.

Summary: The study proves the absence of parity anomaly in M-theory in the low-energy field theory approximation through computational methods. It determines the generators for the 12-dimensional bordism group of pin manifolds with specific characteristics. The study not only solves a specific problem but also demonstrates various computational techniques and algebraic theories.

QUARTERLY JOURNAL OF MATHEMATICS (2021)

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Article Mathematics

Bouquets revisited and equivariant elliptic cohomology

M. Vergne

Summary: The text reviews the construction of bouquets of analytic equivariant cohomology classes and K-integration on a spin manifold with action of a compact Lie group. It introduces elliptic bouquets of germs of holomorphic equivariant cohomology classes on the manifold, and demonstrates that integration of these bouquets is well defined. The systematic use of the Chern-Weil construction of equivariant classes allows the reduction of proofs to algebraic identities.

INTERNATIONAL JOURNAL OF MATHEMATICS (2021)

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L2 curvature bounds on manifolds with bounded Ricci curvature

Wenshuai Jiang et al.

Summary: The paper proves the existence of an L-2 curvature bound for manifolds with bounded Ricci curvature and noncollapsing property, and shows that the singular set of GH-limit manifolds is n-4 rectifiable.

ANNALS OF MATHEMATICS (2021)

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Article Mathematics