Hassan H. Abdallah

activity

20242026

collaborators

4 papers

math.AT2026

On the cobordism groups of $O ⟨ n ⟩$ -manifolds

Hassan H. Abdallah

Given a smooth manifold, a tangential $O ⟨ n ⟩$ -structure is a lift of the classifying map of its tangent bundle to $B O ⟨ n ⟩$ . An $O ⟨ n ⟩$ -manifo…

math.AT2025

The homotopy fixed points of Real spin bordism

Hassan H. Abdallah, Yigal Kamel

We show that the 2-local splitting of spin $^{c}$ bordism by Anderson--Brown--Peterson and Stong refines to a $C_{2}$ -equivariant map in the category of spectra with $C_{2}$ -action from R…

math.AT2025

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

Hassan H. Abdallah, Zachary Halladay, Yigal Kamel

In this note, we show that there does not exist a $C_{2}$ -ring spectrum whose underlying ring spectrum is $MSpin^{c}$ and whose $C_{2}$ -fixed point spectrum is $MSpin$ .

math.AT2024

Products in spin $^{c}$ -cobordism

Hassan Abdallah, Andrew Salch

We calculate the mod $2$ spin $^{c}$ -cobordism ring up to uniform $F$ -isomorphism (i.e., inseparable isogeny). As a consequence we get the prime ideal spectrum of the mod $2$ spin $^{c}$ …

On the cobordism groups of O⟨n⟩-manifolds

The homotopy fixed points of Real spin bordism

On the nonexistence of a Green functor with values spinc bordism and spin bordism

Products in spinc-cobordism

On the cobordism groups of $O ⟨ n ⟩$ -manifolds

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

Products in spin $^{c}$ -cobordism