This page lists corrections to the January, 2008, draft second edition of Introduction to Smooth Manifolds by John M. Lee. Please let me know about any errors, or suggestions for improvement, that you observe. Errors reported to me by students before they are posted here will earn $.25 each from Jack Lee and from me towards refreshments for the last day of class. Current count of errors spotted first by students during 546: 13.
The numbers nn/mm indicate the correction is for page nn, line mm. A negative line number indicates counting up from the bottom of the page. The date posted is listed at the end of the item.
23/-1: Delete everything after "imples that" to the end of the page.
(1/14)
24: In the figure, the shaded region in the lower left should be labeled
with the expression at the start of the first line of text. Similarly
change the same expression at the end of the display in line 3.
In each case, you are replacing the expression deleted at the end of p. 23.
(In TeX, the correction is as follows:
Replace $\phi_\alpha\circ\phi_\beta^{-1}$ by
$(\phi_\beta\circ\phi_\alpha^{-1})^{-1}$ twice, once in the figure and
once in the first displayed equation.) (1/14)
25/-1&-2: Interchange the domains and codomains of
A, B, C, and D. (1/14)
26/1: Interchange the subscripts in each map. For instance,
A should be the projection to P',
restricted to P. (1/14)
31/3: Should say "neighborhood W in Rn"
(1/14)
41/10: Last word in line should be "Proposition" (not "Corollary").
(1/15)
60: Fig. 3.2 caption should refer to sphere with dimension n-1
(to match text below). (1/30)
65/8: Delete second "and". (1/30)
66/-19: Insert "smooth" at start of line, so the line starts
"smooth function on all of M ...". (1/31)
81/1: The subscripts pi should all be the preimage point
p = (p1, ... , pk). (2/1)
90/12: Example 4.12(d) should refer to Example 4.3(c) (not (b)). (2/18)
95/-6: Change second "is" to "if" (so it reads "smooth covering map if ...".
(2/5)
105/-4: In Problem 4-2, add the assumption that M isn't empty.
(1/31)
109/18: Proof should start "We give S a topology ..."
(not "We give N ...". (2/8)
120/12: Add a period at end of line (just before Prop. 5.18). (2/5)
127/6: Add "to" so it reads "it is possible to show that ...". (2/5)
128/-1: Superscript "k=1" should be "k+1". (2/24)
130/1: Add a period at the end of the line, after "proposition." (2/5)
132/12: Delete first appearance of "n-dimensional". (5/28)
146/15: Exercise 6.9 should end with a period. (2/24)
146/-7: Line should begin "function on U" (not on M).
(2/24)
149/4: Change to "The next proposition shows how ..." (insert "how").
(2/18)
151/6: In second display, change X to Y twice. (2/24)
153/9: Change "operation" to "operator." (2/24)
179/16-17: The comment on (7.8) is incorrect. If the LHS is defined,
then the RHS is defined and the equality holds.
The converse is more nuanced, as stated in class. (3/1)
184: In Fig. 7.8, put a break in the curve where the arrowhead is.
(The curve through e and the other point are both integral curves of
X, but not necessarily the same integral curve.) (3/1)
NOTE: The next three corrections apparently are fixing photocopying
errors. The symbols are "t's" in the electronic version.
Similarly on pp. 275-276 and 490 listed below.
190/1-2: The subscripts on the subscripts should be "t's" (not
"i's" or "iota's"). (2/26)
192/-5: The subscripts on the subscripts should be "t's" (not
"i's" or "iota's"). (3/3)
193/Fig. 7.13: In the "middle" tangent plane, the subscript on the subscript
should be "t" (not "i" or "iota"). (3/3)
195/3: Should say "each p in U" (not "in M"). (2/26)
195: In Example 7.29, E1 should just be the coordinate
vector with respect to r (to be a unit vector), and then the bracket
should be corrected to have r2 in the denominator
(instead of r3). (3/1)
205/1: Change "preceding chapter" to "Chapter 6". (2/24)
213/10: Should refer to Chapter 7 instead of Chapter 6. (3/7)
216/-4: Change "will be asked" to "were asked". (3/4)
249/13: The hypothesis of Cor. 9.41 should be that F is a local
diffeomorphism, not just that F is smooth. (The conclusion
is true if F is merely smooth, but the proof is messier,
and we don't need the more general case until later.)(4/9)
262/1: Change T1(V) to
T1(V). (4/4)
273/7: Delete part (d) of Proposition 10.29. This result should be
a Proposition or exercise in Chapter 12 (p. 322 or 323). (4/9)
274/-13: The comma before "It turns out" should be a period. (4/9)
275/5-6: In each of these two lines, there is one "iota" in a subscript
of a subscript which should be a "t". (4/23)
281/8: Insert "of" so line ends "neighborhood of p." (4/25)
282/12: Replace "theorm" by "theorem". (4/16)
301/-13: Paragraph should end "properties of differential forms"
(insert "of"). (4/23)
322/8: Should start "In Chapter 9" (not Chapter 12). (4/23)
369/19: Insert "to" so it reads "In this section, we will use the
Frobenius Theorem to show..." (4/28)
385/-3: Delete "global". (2/28)
386/7: On right side of (15.7), switch order to p dot g.
(5/20)
423: In Problem-21, g is both the Riemannian metric and an element
group of the group; two different symbols should be used. (6/18)
479/3,4: "Integrals" is misspelled.(6/3)
490: Second displayed equation, more subscript"t's"s of subscripts
that appear in our photocopied texts as "iota's". (6/6)
582/-6: Second "X-tilde" should be "S-tilde". (1/11)
604/7: Should say total derivative is equal to the linear map of which
F is a restriction. (1/30)
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