LIP丛嵌入(英文)

LIP BUNDLE EMBEDDINGS

设μ=(E’,j,X)是Lip n-丛,{U1,U2}是X的开复盖,ξ1=(E1,j1,U1)是Lip n-丛,且ξ2=(E2=U2×Rn,P1,U2)是标准平凡Lip n-丛.本文证明了如Fi:Ei→E’|Ui,i=1,2,是由ξi到μ|Ui的Lip丛嵌入,则存在Lipn-从ξ=(E,π,X)满足ξ|(U1-U2)=ξ1|(U1-U2)|且存在由ξ到μ的Lip嵌入F满足F|(E|(U1-U2)=F1|(E1|(U1-U2)).

Assume that (E' ,j,X) is a Lip n-microbundle, {U1,U2} is an open cover of X,ξ= (E1, j, U1) a Lip n-bundle and ξ2 = (E2 = U2×Rn,P1,U2) is the standard trivial Lip n-bundle. This paper proves that if Fi:Ei →E' | Ui,i = 1,2, are Lip bundle embeddings from ξi to μ |Ui | , there is a Lip n-bundle ξ: = (E, π, X ) satisfying ξ |U1-U2)=ξ1 |((U1-U2), and there is a Lip bundle embedding F from ξ to μ satisfying F|(E|(U1-U2))=F1| (E1|(U1-U2)).