Equivariant algebraic topology

Equivariant Algebraic Topology

This paper develops the introductory theory of equivariant algebraic topology. We first define G-CW complexes and prove some basic homotopy-theoretic results Whitehead’s theorem, cellular and CW approximation, and the Freudenthal suspension theorem. We then define ordinary (Bredon) homology and cohomology theories and give an application to Smith theory. Our treatment of this material closely f...

Equivariant Cohomology in Algebraic Geometry Appendix A: Algebraic Topology

HiX and H X = ⊕ H iX. We refer to [Spa66] for the details and basic properties of these constructions, summarizing the most relevant facts below. One sacrifices some geometric intuition in working with cohomology instead of homology, but one gains the advantage of an easily defined ring structure. If σ ∈ CkX is a singular simplex, let fiσ ∈ CiX be the restriction of σ to the front i-face of the...

Categorically-algebraic topology and its applications

This paper introduces a new approach to topology, based on category theory and universal algebra, and called categorically-algebraic (catalg) topology. It incorporates the most important settings of lattice-valued topology, including poslat topology of S.~E.~Rodabaugh, $(L,M)$-fuzzy topology of T.~Kubiak and A.~v{S}ostak, and $M$-fuzzy topology on $L$-fuzzy sets of C.~Guido. Moreover, its respe...

On Equivariant Algebraic Suspension

Equivariant versions of the Suspension Theorem L 1 ] for algebraic cycles on projective varieties are proved. Let G be a nite group, V a projective G-module, and X P C (V) an invariant subvariety. Consider the algebraic join = V 0 X = X#P C (V 0) of X with the regular representation V 0 = C G of G. The main result asserts that algebraic suspension induces a G-homotopy equivalence Z s (X) ?! Z s...

Equivariant Algebraic Geometry