Dr Martin Crossley

Associate Professor, Mathematics

+44 (0) 1792 602759

m.d.crossley@swansea.ac.uk

Office - 304
Third Floor
Computational Foundry
Bay Campus

About

Dr Martin Crossley is an Associate Professor at Swansea University, specializing in algebra and algebraic topology. He is Deputy Head of the Mathematics Department, and a Senior Fellow of the Higher Education Academy.

Prior to arriving in Swansea Martin worked in universities and research institutes in Spain, France and Germany, giving him a very international perspective on mathematics and mathematics education.

Areas Of Expertise

Hopf algebras
Modular representation theory
Cohomology operations
Algebraic completions
Algebraic combinatorics

Career Highlights

Teaching Interests

Martin’s teaching interests focus on algebra and topology, and their inter-relations with other areas of mathematics and applications. His book “Essential Topology” has been adopted by universities across the world, and commended for its accessible style.

Research Award Highlights

Publications

Research Highlights

Crossley, M., Whitehouse, S., & Crossley, M. (2001). Higher conjugation cohomology in commutative Hopf algebras. Proceedings of the Edinburgh Mathematical Society, 44(01), 19
https://doi.org/10.1017/S0013091599000826, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa1622
Clarke, F., Crossley, M., Whitehouse, S., & Crossley, M. (2001). Bases for Cooperations in K-Theory. K-Theory, 23(3), 237-250.
https://doi.org/10.1023/A:1011820819598, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa1623
Clarke, F., Crossley, M., & Whitehouse, S. (2005). Algebras of operations in K-Theory. Topology, 44(1), 151-174.
https://doi.org/10.1016/j.top.2004.05.003, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa1624
Clarke, F., Crossley, M., & Whitehouse, S. (2007). The discrete module category for the ring of K-theory operations. Topology, 46(2), 139-154.
https://doi.org/10.1016/j.top.2007.01.001, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa1625
Crossley, M. & Turgay, N. (2013). Conjugation invariants in the Leibniz–Hopf algebra. Journal of Pure and Applied Algebra, 217(12), 2247-2254.
https://doi.org/10.1016/j.jpaa.2013.03.003, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa13500
Church, T., Crossley, M., Giansiracusa, J., Crossley, M., & Giansiracusa, J. (2012). Invariance properties of Miller-Morita-Mumford characteristic numbers of fibre bundles. The Quarterly Journal of Mathematics
https://doi.org/10.1093/qmath/has029, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa13501
Crossley, M. (2013). GROUP BIALGEBRAS AND PERMUTATION BIALGEBRAS. Glasgow Mathematical Journal, 1-5.
https://doi.org/10.1017/S0017089512000808, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa13502
CROSSLEY, M. & Crossley, M. (2006). Some Hopf algebras of words. Glasgow Mathematical Journal, 48(03), 575
https://doi.org/10.1017/S0017089506003302, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa13503

All Research

Journal Articles

Crossley, M. & Turgay, N. (2013). Conjugation invariants in the Leibniz–Hopf algebra. Journal of Pure and Applied Algebra, 217(12), 2247-2254.
https://doi.org/10.1016/j.jpaa.2013.03.003, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa13500
Crossley, M. (2013). GROUP BIALGEBRAS AND PERMUTATION BIALGEBRAS. Glasgow Mathematical Journal, 1-5.
https://doi.org/10.1017/S0017089512000808, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa13502
Church, T., Crossley, M., Giansiracusa, J., Crossley, M., & Giansiracusa, J. (2012). Invariance properties of Miller-Morita-Mumford characteristic numbers of fibre bundles. The Quarterly Journal of Mathematics
https://doi.org/10.1093/qmath/has029, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa13501
Clarke, F., Crossley, M., & Whitehouse, S. (2007). The discrete module category for the ring of K-theory operations. Topology, 46(2), 139-154.
https://doi.org/10.1016/j.top.2007.01.001, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa1625
CROSSLEY, M. & Crossley, M. (2006). Some Hopf algebras of words. Glasgow Mathematical Journal, 48(03), 575
https://doi.org/10.1017/S0017089506003302, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa13503
Clarke, F., Crossley, M., & Whitehouse, S. (2005). Algebras of operations in K-Theory. Topology, 44(1), 151-174.
https://doi.org/10.1016/j.top.2004.05.003, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa1624
Crossley, M., Whitehouse, S., & Crossley, M. (2001). Higher conjugation cohomology in commutative Hopf algebras. Proceedings of the Edinburgh Mathematical Society, 44(01), 19
https://doi.org/10.1017/S0013091599000826, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa1622
Clarke, F., Crossley, M., Whitehouse, S., & Crossley, M. (2001). Bases for Cooperations in K-Theory. K-Theory, 23(3), 237-250.
https://doi.org/10.1023/A:1011820819598, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa1623

Supervision

Provisional Title: Trusses and Applications of Trusses (current)

PhD

Other supervisor: Prof Tomasz Brzezinski

Taught Modules

MA-004 Fundamental Geometry

This module introduces some essential geometric tools covering the basics of trigonometry, coordinate geometry, vectors and matrices.
MA-312 Higher Algebra

This course approaches the theory of groups, rings and modules as abstract algebraic objects. The course also introduces categories as a language and unifying force in modern mathematics.
MA-322 Topology

This module explores the topological approach to continuity and the study of objects via their topological structure
MA-M22 Topology

This module explores the topological approach to continuity and the study of objects via their topological structure

Dr Martin Crossley

Telephone number

Email address

About

Areas Of Expertise

Career Highlights

Publications

Research Highlights

All Research

Journal Articles

Supervision

Provisional Title: Trusses and Applications of Trusses (current)

Taught Modules

MA-004 Fundamental Geometry

MA-312 Higher Algebra

MA-322 Topology

MA-M22 Topology