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math.GT2025

4-manifolds with a given boundary

Anthony Conway, Daniel Kasprowski

This paper studies the homotopy and homeomorphism classifications of -manifolds with boundary. Given -manifolds and with fundamental group , we consider the p…

math.GT2025

The first relative k-invariant

Anthony Conway, Daniel Kasprowski

Motivated by work on the homotopy classification of -manifolds with boundary, we define a relative -invariant for pairs of spaces that are homotopy equivalent to CW pairs. We…

math.GT2025

Stably exotic 4-manifolds

Daniel Kasprowski, Mark Powell

A pair of closed, smooth -manifolds and are stably exotic if they are stably homeomorphic but not stably diffeomorphic, where stabilisation refers to connected sum with…

math.GT2025

Homotopy classification of -manifolds with -manifold fundamental group

Jonathan Hillman, Daniel Kasprowski, Mark Powell +1

We give a criterion on a group and a homomorphism under which closed -manifolds with fundamental group and orientation character are classifie…

math.GT2025

Immersions of punctured 4-manifolds: with applications to Quantum Cellular Automata

Michael Freedman, Daniel Kasprowski, Matthias Kreck +2

Motivated by applications to pulling back quantum cellular automata from one manifold to another, we study the existence of immersions between certain smooth 4-manifolds. We show t…

math.GT2024

The Kervaire-Milnor invariant in the stable classification of spin 4-manifolds

Daniel Kasprowski, Mark Powell, Peter Teichner

We consider the role of the Kervaire--Milnor invariant in the classification of closed, connected, spin 4-manifolds, typically denoted by , up to stabilisation by connected sums…