Differential Forms, 2nd Edition

Index

A

alternation, 57

atlas, 146, 158

smooth, 147–148

B

brick, 160, 198

C

Cartan, Elie, 47

chain homotopy, 299

chain, smooth, 202

chocolate, 108

co/contravariant, 101, 122

coboundary, 302, 311

coboundary map, 365

cochain, 311, 365

cochain complex, 365

map of, 366

cocycle, 365

cohomology group, 365

contractible, smoothly, 203

contraction, 77

coordinate chart(s), 158

compatible, 147

cotangent vector field, 56

curl, 34

D

de Rham cohomology, 361

induced map on, 372

Mayer-Vietoris theorem in, 381–382

Poincaré duality in, 389

product on, 378

properties of, 377

relative, 373

with compact supports, 361

de Rham’s Theorem, 348

determinant, 72, 86

diffeomorphism, 147

orientation preserving/reversing, 186, 195

differential ...