Quasi-theories and their equivariant orthogonal spectra

Abstract

In this paper we construct orthogonal G−spectra up to a weak equivalence for the quasi-theory QE * n,G (−) corresponding to certain cohomology theories E. The construction of the orthogonal G−spectrum for quasielliptic cohomology can be applied to the constructions for quasi-theories.

Almost Global Homotopy Theory

“…In [13] we construct a I G −FSP representing quasi-elliptic cohomology up to a weak equivalence, which, however, cannot arise from an orthogonal spectrum. In [17] we apply the idea to construct a I G −FSP weakly representing each quasi-theory QE * n,G (−). In this section we show these I G −FSP together define a D W 0 −spectrum.…”

“…In this section we show the construction of a D C −spectrum representing the theory QE * n,G (−). The details of the construction are in Section 5 [17] with the main conclusion Theorem 5.18. Another reference is Chapter 4 [14].…”

“…We sketch the construction of the I G −FSP (QE n (G, −), η QEn , µ QEn ) below. For more details please see [17].…”

“…Given a unitary global spectrum representing E, we can also construct a unitary D W 0 −spectrum representing QE * n the same way described in this section. The complex Λ G (σ)−representations needed in the construction is constructed in Section A.1 [17]. Remark 6.10.…”

“…Quasi-theories {QE * n,G (−)} G have the change-of-group isomorphism if the initial theory {E * G (−)} G does, as shown in [16]. In [17] we construct an orthogonal G−spectrum for each quasi-theory. The construction generalizes that for quasielliptic cohomology in [13].…”