Local structures on stratified spaces

详细信息    查看全文

• 作者：David Ayala^a ; ^{david.ayala@montana.edu} ; John Francis^b ; ^{jnkf@northwestern.edu} ; Hiro Lee Tanaka^c ; ^{hirolee@math.harvard.edu}
• 关键词：primary ; 57N80 ; secondary ; 57P05 ; 32S60 ; 55N40 ; 57R40
• 刊名：Advances in Mathematics
• 出版年：2017
• 出版时间：5 February 2017
• 年：2017
• 卷：307
• 期：Complete
• 页码：903-1028
• 全文大小：1636 K
• 卷排序：307

文摘

We develop a theory of conically smooth stratified spaces and their smooth moduli, including a notion of classifying maps for tangential structures. We characterize continuous space-valued sheaves on these conically smooth stratified spaces in terms of tangential data, and we similarly characterize 1-excisive invariants of stratified spaces. These results are based on the existence of open handlebody decompositions for conically smooth stratified spaces, an inverse function theorem, a tubular neighborhood theorem, an isotopy extension theorem, and functorial resolutions of singularities to smooth manifolds with corners.