Twists of K-theory and TMF

By M. Ando, Andrew Justin Blumberg, D. Gepner. 2010

66 citations recorded by the source corpus.

We explore an approach to twisted generalized cohomology from the point of view of stable homotopy theory and quasicategory theory provided by arXiv:0810.4535. We explain the relationship to the twisted K-theory provided by Fredholm bundles. We show how our approach allows us to twist elliptic cohomology by degree four classes, and more generally by maps to the four-stage Postnikov system BO . We also discuss Poincare duality and umkehr maps in this setting.

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/79d9ece1c6f7afb852c3fafb07e9100c79c10f6d

Citations in the corpus

• Units of ring spectra, orientations, and Thom spectra via rigid infinite loop space theory (2014, unknown): “ps X→ BGL1R; the ones which arise from Thom spectra of spherical fibrations are the ones which factor as in (1.11). We discuss the relationship to other approaches to twisted generalized cohomology in [4]. 1.5. Historical remarks and related work. In his 1970 MIT notes [41],1 Sullivan introduced the ”
• An ∞‐categorical approach to R‐line bundles, R‐module Thom spectra, and twisted R‐homology (2014, unknown): “In [ 1 ], we prove that there is an equivalence of ∞ -categories between the simplicial nerve of the May–Sigurdsson category of parameterized orthogonal spectra N( S cf X ) and the ∞ -category Fun( X op , Stab(Gpd ∞ )).”