Conjugation spaces and edges of compatible torus actions

Conjugation spaces and 4-manifolds

“…There is a ring isomorphism κ : H 2 * (X; Z 2 ) ∼ = H * (X G ; Z 2 ) dividing the degrees in half, where X G denotes the fixed set under the involution. The structure underlying this property was discovered by Hausmann, Holm and Puppe [23], and studied further in [16,22,35,36,37]. A G-space with this structure is a conjugation space (see Section 2 for the precise definition).…”

Involutions onS6with 3–dimensional fixed point set

“…Recently, a class of involutions called conjugations was defined in [HHP05] and various aspects of conjugations were studied in [FP05,Olb07,HH08,HH09]. Conjugations τ on topological spaces X have the property that the fixed point set has Z 2 -cohomology ring isomorphic to the Z 2 -cohomology ring of X, with the slight difference that all degrees are divided by two.…”