Frederick R. Cohen

Short description: American mathematician (1945–2022)

Fred Cohen

Born| 1945

Chicago

Died| January 16, 2022
Alma mater| University of Chicago
Known for| topology of configuration spaces
calculation of homotopy groups of spheres
polyhedral products
Awards| Sloan Research Fellow
Fellow of the AMS
Scientific career
Fields| Mathematics
Institutions| University of Rochester
Thesis| The Cohomology of Braid Spaces (1972)
Doctoral advisor| J. Peter May
Website| https://people.math.rochester.edu/faculty/cohf/

Frederick Ronald Cohen[1] (1945 – January 16, 2022)[2][3] was an American mathematician working in algebraic topology.

## Contents

* 1 Education and career
* 2 Mathematics
* 2.1 Selected publications
* 3 Personal life
* 4 References

## Education and career

Fred Cohen was born in 1945 in Chicago . He received a BA from Brandeis University in 1967 and a PhD from the University of Chicago in 1972. He taught at the University of Northern Illinois until 1979 and then at the University of Kentucky. In 1989, he settled at the University of Rochester, where he spent the rest of his career.[2][4]

## Mathematics

Cohen did influential work in several areas of homotopy theory. His thesis concerned the topology of configuration spaces, a topic he came back to throughout his life, with connections to braid groups and mapping class groups. This was followed by a series of influential papers on unstable homotopy groups of spheres with John Moore and Joseph Neisendorfer.[5] Late in his life, Cohen studied polyhedral products in a series of articles with Bahri, Bendersky, and Gitler.[6]

### Selected publications

* Cohen, Frederick R.; Lada, Thomas J.; May, J. Peter (1976). The homology of iterated loop spaces. Lecture Notes in Mathematics. 533. Berlin: Springer-Verlag. doi:10.1007/BFb0080464. ISBN 3540379851.
* Cohen, Frederick R.; Moore, John C.; Neisendorfer, Joseph A. (January 1979). "Torsion in homotopy groups". The Annals of Mathematics 109 (1): 121–168. doi:10.2307/1971269.
* Cohen, Frederick R.; Moore, John C.; Neisendorfer, Joseph A. (November 1979). "The double suspension and exponents of the homotopy groups of spheres". The Annals of Mathematics 110 (3): 549–565. doi:10.2307/1971238.
* Bahri, Anthony; Bendersky, Martin; Cohen, Frederick R.; Gitler, Samuel (October 2010). "The polyhedral product functor: A method of decomposition for moment-angle complexes, arrangements and related spaces". Advances in Mathematics 225 (3): 1634–1668. doi:10.1016/j.aim.2010.03.026.

## Personal life

In the late 1970's, Cohen battled a spinal tumor. Although he survived with the help of radiation therapy, he was partially paralyzed for the rest of his life. Starting in 2013, he used a wheelchair.[2]

Cohen was survived by his wife Kathleen and two daughters.[3]

## References

1. ↑ "Frederick Ronald Cohen". North Dakota State University. https://www.genealogy.math.ndsu.nodak.edu/id.php?id=6654.
2. ↑ 2.0 2.1 2.2 "Frederick R. Cohen, professor of mathematics has passed away". University of Rochester Department of Mathematics News & Events. January 21, 2022. https://www.sas.rochester.edu/mth/news-events/archive/2022-01-21-fred-cohen.html.
3. ↑ 3.0 3.1 "Dr. Frederick R. Cohen Obituary". Rochester Democrat and Chronicle. January 17, 2022. https://www.democratandchronicle.com/obituaries/rdc167894.
4. ↑ "Marquis Who's Who Honors Frederick R. Cohen, PhD, with Inclusion in Who's Who in the World" (in en). 24-7 Press Release Newswire. November 9, 2020. https://www.24-7pressrelease.com/press-release/477078/marquis-whos-who-honors-frederick-r-cohen-phd-with-inclusion-in-whos-who-in-the-world.
5. ↑ Levi, Ran (7 April 2009). "The work of Fred Cohen". Geometry & Topology Monographs 13: 529–546. doi:10.2140/gtm.2008.13.529.
6. ↑ Bahri, Anthony; Bendersky, Martin; Cohen, Frederick R. (2019). "Chapter 3: Polyhedral products and features of their homotopy theory". Handbook of homotopy theory. Boca Raton, Florida: Chapman and Hall/CRC. ISBN 9781351251624. https://www.taylorfrancis.com/chapters/edit/10.1201/9781351251624-3/polyhedral-products-features-homotopy-theory-anthony-bahri-martin-bendersky-frederick-cohen.

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