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2 Nov 2019: B(t) = log A(t) = [B1,B2]t2 o(t2) and exp(B(t) = A(t). ... But thenalso limt0 B(t)/t. 2 = limt0([B1,B2] o(1)) = [B1,B2] g (as g is a closed subset ofmatrices).

4 Apr 2019: dn. Then we have det(B) = d1. dn,while OL/I = ni=1Z/diZ. ... r(π2)s t. n. n! This can be proved by induction. on r,s, the base cases being B1,0(t) = [t, t] and B0,1(t) = D(0, t2 )

8 Nov 2019: a(t) = (t, 1). and b = b1 b2 b3, where. ... b1(t) = (0, 1 t), b2(t) = (t, 0), b3(t) = (1,t).

27 Oct 2019: its base point (so b0 = π and b1 sends all of E to B). ... A morphism from π1 : E1 B1to π2 : E2 B2 comprises a G-equivariant map fE : E1 E2 covering a map fB : B1 B2.

2 Dec 2019: Clearly the intersection of two boxes isa box and if B1 Ă B2 are boxes, then B2zB1 is a finite union of disjoint boxes.(a) follows. ... prove it forone box, say E “ B1 “ I1 ˆ ˆ Id, and this case is easily checked by refiningthe partition pB1jqj