DIAGRAM COHOMOLOGY AND ISOVARIANT HOMOTOPY 75

isotropy depth, 38

isotropy family (of subgroups, sense of torn Dieck), SEE: open isotropy family

isovariant, citation for first use of term in the literature, 1

isovariant homotopy extension property, normally straightened, 32

, weak, 34 (c/. Prop. 4.9 and the preceding discussion)

isovariant Whitehead Theorems ( = Thm. 4.10 and Cors. 4.11-12), 34-37

knot invariant, 70

list of isotropy subgroups (sense of S. J. Willson), 5 ALSO SEE: open isotropy

family

local normal degree, 36

M^Sing(M), SEE: X^Sing(X)

Na(s) (:= e-constriction of 7Va), 14

nested fixed set quasistratification, 14

NH(X) (:= tubular neighborhood for singular

subset inclusion Sing(X^) C XH), 19

NH(X,e) (:= ^-constriction of the preceding object), 19

normal degree, local, 36

normally straightened (mapping), 31

N(Smg(M)) (:= tubular neighborhood of Sing(M) q.v.), 38

open isotropy family (of subgroups, sense of torn Dieck), 5

Or bo (:= usual orbit category of a group), 5, 9

Orb(D) (:= orbit category of a small category), 9

orbit category, usual, 9

orbit subcategory (for a small category), 9

, free, 10

GK*(Y)

(:= coefficient system of homotopy groups

n*(YH)

for

YH

e FY (q.v.) ), 5

Q C

M

, 48

QC&, 48

Q(e) (:= e-constriction of the prestratification Q), 14

Q F

X

, 20-21

Q P (:= quasistratified resolution of P), 20

quasistratification, 12

, G-invariant, 13

, nested fixed set, 14

, regular invariant, 15

quasistratified resolution, 20

Qx (:= some quasistratification of X), 19

Qx(e) (:= e-constriction of the preceding object), SEE: Qx AND Q(e)