Bott suspension and Weyl traces

Two readings connect elliptic indices and phase-space symbols to concrete operators. The Bott reading builds the index-one oscillator, proves suspension along a Euclidean vector bundle, and carries an elliptic index from a compact manifold to Euclidean space. The Weyl reading proves the exact Hilbert–Schmidt kernel map, the phase-space trace identity and a finite trace-class test.

The Bott operator and suspension

Read the Bott lesson · 47-page PDF (being refreshed) · Editable TeX (being refreshed) · Markdown source

The proof retains the original graph domains, exterior-algebra signs, bundle charts, half-density transport, supported kernels and every symbol factor. Identified editorial material proves the sharp full and parity graph bounds and supplies the complete prerequisite receivers.

Weyl kernels and traces

Read the trace lesson · 13-page PDF · Editable TeX · Markdown source

The proof keeps the original Fourier coefficient, matrix rank, signed Gaussian eigenvalues and oscillator domain. It includes the exact trace-class threshold of the original rational Weyl symbol and an editorial proof of the differentiation and integral inputs.

Complete prerequisite proofs and exact receiving passages · Offline reader and complete source · Build instructions · Checksums

Part of Elliptic Operators & Boundary Problems. The two principal lessons and the retained historical supporting components are CC0.

Authors, human sources and component terms · Source identities · Dependency manifest