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763 modules for plain $n$-categories or $A_\infty$ $n$-categories. |
763 modules for plain $n$-categories or $A_\infty$ $n$-categories. |
764 In the plain case we require |
764 In the plain case we require |
765 |
765 |
766 \xxpar{Pseudo and extended isotopy invariance in dimension $n$:} |
766 \xxpar{Pseudo and extended isotopy invariance in dimension $n$:} |
767 {Let $M$ be a marked $n$-ball and $f: M\to M$ be a homeomorphism which restricts |
767 {Let $M$ be a marked $n$-ball and $f: M\to M$ be a homeomorphism which restricts |
768 to the identity on $\bd M$ and is pseudo-isotopic or extended isotopic (rel boundary) to the identity. |
768 to the identity on $\bd M$ and is extended isotopic (rel boundary) to the identity. |
769 Then $f$ acts trivially on $\cM(M)$.} |
769 Then $f$ acts trivially on $\cM(M)$.} |
770 |
770 |
771 \nn{need to rephrase this, since extended isotopies don't correspond to homeomorphisms.} |
771 \nn{need to rephrase this, since extended isotopies don't correspond to homeomorphisms.} |
772 |
772 |
773 We emphasize that the $\bd M$ above means boundary in the marked $k$-ball sense. |
773 We emphasize that the $\bd M$ above means boundary in the marked $k$-ball sense. |