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- Mikhail Khovanov

Discipline name
D-index
D-index (Discipline H-index) only includes papers and citation values for an examined
discipline in contrast to General H-index which accounts for publications across all
disciplines.
Citations
Publications
World Ranking
National Ranking

Mathematics
D-index
32
Citations
8,670
81
World Ranking
2306
National Ranking
971

- Pure mathematics
- Algebra
- Vector space

His primary areas of investigation include Pure mathematics, Algebra, Categorification, Homology and Diagrammatic reasoning. His study in Khovanov homology, Cohomology, Invariant and Braid group falls within the category of Pure mathematics. The Algebra study combines topics in areas such as Calculus and Calculus.

His Categorification research includes elements of 2-category and Algebra over a field, Root datum. In his study, which falls under the umbrella issue of Homology, Representation theory, Linear algebra and Hypersurface is strongly linked to Euler characteristic. Within one scientific family, Mikhail Khovanov focuses on topics pertaining to Discrete mathematics under Cellular homology, and may sometimes address concerns connected to Relative homology.

- A categorification of the Jones polynomial (826 citations)
- Matrix factorizations and link homology (540 citations)
- A diagrammatic approach to categorification of quantum groups II (440 citations)

His primary scientific interests are in Pure mathematics, Categorification, Algebra, Homology and Functor. His Pure mathematics study frequently links to other fields, such as Discrete mathematics. His work carried out in the field of Categorification brings together such families of science as Hecke algebra, Symmetric group and Lie algebra.

His Algebra research integrates issues from Algebra over a field and Calculus. His Functor study combines topics from a wide range of disciplines, such as Vector space, Morphism and Grothendieck group. Mikhail Khovanov interconnects Bracket polynomial, Derived category, Combinatorics and Quantum algebra in the investigation of issues within Cohomology.

- Pure mathematics (68.60%)
- Categorification (38.02%)
- Algebra (30.58%)

- Pure mathematics (68.60%)
- Homology (18.18%)
- Equivariant map (3.31%)

His main research concerns Pure mathematics, Homology, Equivariant map, Functor and Tensor. His study in Cobordism, Categorification, Morphism, Vector space and Special functions falls under the purview of Pure mathematics. His Categorification studies intersect with other subjects such as Diagrammatic reasoning and Reciprocity.

Mikhail Khovanov has researched Homology in several fields, including Formal group and Graph. His study focuses on the intersection of Tensor and fields such as Series with connections in the field of Algebra over a field. His research integrates issues of Homotopy category and Algebra in his study of Algebra over a field.

- Link homology and Frobenius extensions II (16 citations)
- Foam evaluation and Kronheimer--Mrowka theories (8 citations)
- A deformation of Robert-Wagner foam evaluation and link homology (6 citations)

- Pure mathematics
- Algebra
- Vector space

Mikhail Khovanov mainly focuses on Pure mathematics, Homology, Equivariant map, Categorical variable and Algebra over a field. As part of his studies on Homology, he often connects relevant areas like Formal group. His Categorical variable research incorporates a variety of disciplines, including Braid group, Duality, Action, Action and Algebra.

His research on Algebra over a field often connects related topics like Homotopy category.

This overview was generated by a machine learning system which analysed the scientist’s body of work. If you have any feedback, you can contact us here.

A categorification of the Jones polynomial

Mikhail Khovanov.

Duke Mathematical Journal **(2000)**

1425 Citations

A diagrammatic approach to categorification of quantum groups II

Mikhail Khovanov;Aaron D. Lauda.

Transactions of the American Mathematical Society **(2010)**

908 Citations

Matrix factorizations and link homology

Mikhail Khovanov;Lev Rozansky.

Fundamenta Mathematicae **(2008)**

860 Citations

Quivers, Floer cohomology, and braid group actions

Mikhail Khovanov;Paul Seidel.

Journal of the American Mathematical Society **(2001)**

438 Citations

A functor-valued invariant of tangles

Mikhail Khovanov.

Algebraic & Geometric Topology **(2002)**

428 Citations

A diagrammatic approach to categorification of quantum groups III

Mikhail Khovanov;Aaron D. Lauda.

arXiv: Quantum Algebra **(2008)**

427 Citations

Matrix factorizations and link homology II

Mikhail Khovanov;Lev Rozansky.

Geometry & Topology **(2008)**

405 Citations

sl(3) link homology

Mikhail Khovanov.

Algebraic & Geometric Topology **(2004)**

312 Citations

Canonical bases in tensor products and graphical calculus for Uq(2)

Igor B. Frenkel;Mikhail G. Khovanov.

Duke Mathematical Journal **(1997)**

290 Citations

Triply-graded link homology and Hochschild homology of Soergel bimodules

Mikhail Khovanov.

International Journal of Mathematics **(2007)**

276 Citations

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