Differential geometry — forms, de Rham cohomology, flows, and degree

The declarations the status of Tau Ceti's roadmap names, and the other results named in the modules where only this status names declarations, or in folders below the areas where only it names 2 or more, as Tau Ceti has them at commit ace60277.

TauCeti.integralTopForm_mextDeri… to Stokes' formula for a homotopy…

• TauCeti.integralTopForm_mextDeriv
• TauCeti.Green.green_ac_winding
• The Mayer–Vietoris short exact sequence of de Rham complexes
• The Mayer–Vietoris connecting map through a cut-off function
• The compactly supported Mayer–Vietoris short exact sequence
• Homotopy invariance of de Rham cohomology
• The de Rham cohomology of a normed space vanishes in positive degrees
• TauCeti.nontrivial_deRhamCohomology_circle_one
• TauCeti.homotopyOperator
• The cochain-homotopy identity for the homotopy operator on the cylinder M × [0, 1]
• TauCeti.compactlySupportedDeRhamCohomology
• TauCeti.compactlySupportedDeRhamCohomology.extendByZero
• TauCeti.compactlySupportedDeRhamCohomology.integral
• TauCeti.poincarePairing
• TauCeti.pathIntegral
• The fundamental theorem of calculus for line integrals, for a C¹ form ψ of degree zero
• TauCeti.integralTopForm_mpullback_Icc_eq_pathIntegral
• The compactly supported Poincaré lemma on the line
• The fundamental theorem of calculus for path classes
• Stokes' formula for a homotopy of maps of a rectangle

Stokes' theorem on singular…

• Stokes' theorem on singular 1-chains

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