2026 Martin Scharlemann: Mathematics Researcher – H-Index, Publications & Awards

Discipline name	D-Index	World Ranking	Current World Ranking	National Ranking	Current National Ranking	Publications	Citations
Mathematics	31	3397	3035	1326	1109	125	2995

Discipline name

D-Index

World Ranking

Current World Ranking

National Ranking

Current National Ranking

Publications

Citations

Mathematics

3397

3035

1326

1109

125

2995

Research.com Recognitions

2014 - Fellow of the American Mathematical Society For contributions to low-dimensional topology and knot theory.

Overview

Martin Scharlemann is a researcher affiliated with the University of California, Santa Barbara, United States. Their primary field of study is Mathematics, with a specialized focus on Geometry and Topology. Their work spans multiple subfields including Mathematical Physics, Discrete Mathematics and Combinatorics, Applied Mathematics, and Algebra and Number Theory.

The researcher's main topics of study include:

Geometric and Algebraic Topology
Mathematical Dynamics and Fractals
Finite Group Theory Research
Homotopy and Cohomology in Algebraic Topology
Advanced Algebra and Geometry
Functional Equations Stability Results
Advanced Topics in Algebra

Scharlemann's recent scholarly contributions include the following papers:

"Uniqueness in Haken's Theorem," 2022, published in The Michigan Mathematical Journal
"A strong Haken theorem," 2024, published in Algebraic & Geometric Topology
"A Strong Haken's Theorem," 2020, available on arXiv (Cornell University)
"One Powell generator is redundant," 2020, published in Proceedings of the American Mathematical Society Series B
"Powell's Conjecture on the Goeritz group of S3 is stably true," 2022, available on arXiv (Cornell University)

The frequent publication venues for Scharlemann's work include:

arXiv (Cornell University)
Algebraic & Geometric Topology
The Michigan Mathematical Journal
Proceedings of the American Mathematical Society Series B
Journal of the Association for Mathematical Research

Collaborative work features frequent coauthors such as Michael J. Freedman and Michael Freedman.

In recognition of their contributions, Scharlemann was named a Fellow of the American Mathematical Society in 2014 for work in low-dimensional topology and knot theory.

Best Publications

Producing reducible 3-manifolds by surgery on a knot

Martin Scharlemann

229
Citations
Heegaard splittings of (surface) x I are standard

Martin Scharlemann;Abigail Thompson

193
Citations
Sutured manifolds and generalized Thurston norms

Martin Scharlemann

175
Citations
Link genus and the Conway moves

Martin Scharlemann;Martin Scharlemann;Abigail Thompson;Abigail Thompson

137
Citations
Unknotting number one knots are prime.

Martin G. Scharlemann

134
Citations
Local detection of strongly irreducible Heegaard splittings

Martin Scharlemann

117
Citations
Alternate Heegaard genus bounds distance

Martin Scharlemann;Maggy Tomova

117
Citations
Comparing Heegaard splittings of non-haken 3-manifolds

Hyam Rubinstein;Martin Scharlemann

115
Citations
Thin position for 3-manifolds

Unknown

108
Citations
Heegaard splittings of compact 3-manifolds

Martin Scharlemann

101
Citations
Smooth spheres in ℝ4 with four critical points are standard

Martin Scharlemann

96
Citations
AUTOMORPHISMS OF THE 3-SPHERE THAT PRESERVE A GENUS TWO HEEGAARD SPLITTING

Martin Scharlemann

92
Citations
Thin position and Heegaard splittings of the 3-sphere

Martin Scharlemann;Abigail Thompson

84
Citations
Tunnel number one knots satisfy the poenaru conjecture

Martin Scharlemann

74
Citations
Proximity in the curve complex: boundary reduction and bicompressible surfaces

Martin Scharlemann

66
Citations
Unknotting number, genus, and companion tori

Martin Scharlemann;Abigail Thompson

63
Citations
Detecting unknotted graphs in 3-space

Martin Scharlemann;Abigail Thompson

61
Citations
Finding Disjoint Seifert Surfaces

Martin Scharlemann;Abigail Thompson

61
Citations
THE TUNNEL NUMBER OF THE SUM OF n KNOTS IS AT LEAST n

Martin Scharlemann;Jennifer Schultens

58
Citations
Levelling an unknotting tunnel

Hiroshi Goda;Martin Scharlemann;Abigail Thompson

58
Citations
Thin Position in the Theory of Classical Knots

Martin Scharlemann

53
Citations
EIGHT FACES OF THE POINCARE HOMOLOGY 3-SPHERE

R.C. Kirby;M.G. Scharlemann

35
Citations
Chapter 18 – Heegaard Splittings of Compact 3-Manifolds

Martin Scharlemann

20
Citations

Frequent Co-Authors

Michael H. Freedman University of California, Santa Barbara

Matt Jones University of Bristol

External Links

Personal website of Martin Scharlemann

If you think any of the details on this page are incorrect, let us know.

Related Online Degrees & Career Pathways

For those studying Mathematics in the USA, exploring related online degrees can open diverse career opportunities. Finance professionals, for instance, benefit greatly from affordable education options, making the cheapest online masters in finance a popular choice for advancing quantitative skills beyond pure mathematics.

Entrepreneurship and leadership roles are also within reach through accelerated management programs. The shortest MBA program online offers a streamlined curriculum for those looking to quickly boost their business acumen without long-term commitment.

In marketing, an area increasingly reliant on data analytics, obtaining an MS in digital marketing degree cost tuition fees reveal programs that balance affordability with excellent earning potential, ideal for mathematically inclined students aiming to enter this dynamic field.

Additionally, students can accelerate their career trajectory by pursuing a one year MBA, which combines comprehensive business education with the flexibility of online learning, perfect for those who want to merge analytical skills with managerial expertise.