Universal Embedding spaces for G-manifolds

2024/12/31 by Arthur Wasserman, Wasserman, Arthur G.
Computer Science · Mathematics · #57R91(secondary) #57S15(primary) #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2501.00624

openalex publication_date 2024/12/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For any compact Lie group G and any n we construct a smooth G-manifold U_n(G) such that any smooth n-dimensional G-manifold can be embedded in U_n(G) with a trivial normal bundle. Furthermore, we show that such embeddings are unique up to equivariant isotopy It is shown that the (inverse limit) of the cohomology of such spaces gives rise to natural classes which are the analogue for G-manifolds of characteristic classes for ordinary manifolds. The cohomotopy groups of U_n(G) are shown to be equal to equivariant bordism groups.

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