Errata for the book: Natural operations in differential geometry

# Misprints in the book: Natural operations in differential geometry, by Kolár, Ivan; Slovák, Jan; Michor, Peter W.

August 14, 1997

Please, send any other misprints to <Peter.Michor@esi.ac.at>

• p 70, Lemma 8.6 second equation, a sign mistake: $[i_L,\Cal L_K] = \Cal L(i_LK) + (-1)^{k}i([L,K])$
• p 79: Lemma 9.7 could be clearer. After the lemma, insert the sentences:
By $[\Gamma^\alpha,\Gamma^\alpha]_{\frak X(S)}$ we just mean the 2-form $(\xi,\eta)\mapsto [\Gamma^\alpha(\xi),\Gamma^\alpha(\eta)] \in \frak X(S)$. See 11.2 for the more sophisticated expression $\frac 12 [\Gamma^\alpha,\Gamma^\alpha]_\wedge$.
• p 102: (7) a sign mistake ... so $\Gamma^\alpha(\xi_x) = - R_{\omega_\alpha(\xi_x)}$
• p 103: (10) a sign mistake Then we have $\zeta_{d_\omega\psi} = - [\Phi,\zeta_\psi]$.
• p 105: in the last display of the proof of (10): put $-$ in front of all 3 expressions.
• p 306 line 17 As in step 1 we see ...
After July 23, 2003
• p 40 line14: a sign mistake in the last expression for the Baker-Campbell-Hausdorff formula: $= X + Y + \tfrac12[X,Y] +\tfrac1{12}([X,[X,Y]]+[Y,[Y,X]]) + \cdots$
• p 5 line 8: Replace separable' by $\sigma$-compact (a countable union of compact subsets); equivalently second contable.' A counterexample for separable is in: [Mary Ellen Rudin. Two nonmetrizable manifolds. Topology and its Appl., 35:137-152, 1990]