Embeddings in the 3/4 range

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• 作者：Brian A. Munson
• 关键词：Embedding ; Calculus of functors
• 刊名：Topology
• 出版年：2005
• 期刊代码：59_00409383
• 类别：mt
• 出版时间：2005
• 卷：44
• 期：6
• 页码：1133-1157
• 文件大小：532 K

摘要

We give a complete obstruction to turning an immersion <a name="mml10">a><a style="text-decoration:none; color:black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6V1J-4GGWG74-1&_mathId=mml10&_user=10&_cdi=5676&_rdoc=3&_handle=V-WA-A-W-E-MsSAYVW-UUW-U-AABZBUYWWC-AABBYYEUWC-CADDVABAE-E-U&_acct=C000050221&_version=1&_userid=10&md5=44e7e7053cd25944fd2e12df6bb85dc7" title="Click to view the MathML source">f:M^m→Rⁿa> into an embedding when <a name="mml11">a><a style="text-decoration:none; color:black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6V1J-4GGWG74-1&_mathId=mml11&_user=10&_cdi=5676&_rdoc=3&_handle=V-WA-A-W-E-MsSAYVW-UUW-U-AABZBUYWWC-AABBYYEUWC-CADDVABAE-E-U&_acct=C000050221&_version=1&_userid=10&md5=9e4020a593d467d6bca46bf0193cc50b" title="Click to view the MathML source">3nc="http://www.sciencedirect.com/scidirimg/entities/2a7e.gif" alt="greater-or-equal, slanted" border=0>4m+5a>. It is a secondary obstruction, and exists only when the primary obstruction, due to André Haefliger, vanishes. The obstruction lives in a twisted cobordism group, and its vanishing implies the existence of an embedding in the regular homotopy class of f in the range indicated. We use Tom Goodwillie's calculus of functors, following Michael Weiss, to help organize and prove the result.