The equivariant Spivak normal bundle and equivariant surgery for compact Lie groups

2017/05/31 by Steven R. Costenoble, Costenoble, Steven R., Stefan Waner +1
Mathematics · Medicine · #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Ophthalmology and Eye Disorders

paper · pdf · doi:10.48550/arxiv.1705.10909

openalex publication_date 2017/05/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We generalize the results of a previous paper of ours to compact Lie groups. Using a recently developed ordinary equivariant homology and cohomology, we define equivariant Poincare complexes with the properties that (1) every compact G-manifold is an equivariant Poincare complex, (2) every finite equivariant Poincare complex (with some mild additional hypotheses) has an equivariant spherical Spivak normal fibration, and (3) the Pi-Pi Theorem holds for equivariant Poincare pairs under suitable gap hypotheses. The nice behavior of the ordinary equivariant homology and cohomology theories allows us to follow Wall's original line of argument closely.

Related

• Equivariant ordinary homology and cohomology
• On Equivariant Poincaré Duality, Gysin Morphisms and Euler Classes
• Equivariant K-theory for proper actions of non-compact Lie groups
• Formal Frobenius manifold structure on equivariant cohomology
• A Geometric Approach to Equivariant Factorization Homology and Nonabelian Poincaré Duality