Work

On the nonexistence of a Green functor with values $$\hbox {spin}^c$$ bordism and spin bordism

Year: 2026

Type: article

Abstract: We show that there does not exist a $$C_2$$ C 2 -ring spectrum whose underlying ring spectrum is $$\textrm{MSpin}^c$$ MSpin c and whose $$C_2$$ C 2 -fixed point spectrum is $$\textrm{MSpin}$$ MSpin . As a corollary, the $$\hbox {spin}^c$$ spin c and spin orientations of Atiyah–Bott–Shapiro cannot be obtained as the underlying and fixed point maps of a single map of $$C_2$$ C 2 -ring spectra.

Source: Archiv der Mathematik

DOI: 10.1007/s00013-026-02229-y

Authors: Hassan H. Abdallah, Zachary Halladay, Yigal Kamel

Institutions: Wayne State University, University of Illinois Urbana-Champaign

Language: English

Topic: Homotopy and Cohomology in Algebraic Topology

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

OpenAlex ID: W7142847870