The homotopy type of the cobordism category

• 成果类型: Article
• 署名作者: Galatius, Soren; Madsen, Ib; Tillmann, Ulrike; Weiss, Michael
• 署名单位: Stanford University; University of Copenhagen; University of Oxford; University of Aberdeen
• 刊物名称: ACTA MATHEMATICA
• ISSN/ISSBN: 0001-5962
• DOI: 10.1007/s11511-009-0036-9
• 发表日期: 2009
• 页码: 195-239
• 关键词: mapping class group; SURFACES; STABILITY; HOMOLOGY; SPACE

摘要

The embedded cobordism category under study in this paper generalizes the category of conformal surfaces, introduced by G. Segal in [S2] in order to formalize the concept of field theories. Our main result identifies the homotopy type of the classifying space of the embedded d-dimensional cobordism category for all d. For d = 2, our results lead to a new proof of the generalized Mumford conjecture, somewhat different in spirit from the original one, presented in [MW].