Boris L Tsygan

  • 481 Citations
1983 …2019

Research output per year

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Research Output

  • 481 Citations
  • 31 Article
  • 4 Conference contribution
  • 3 Chapter
  • 1 Editorial
2018

A microlocal category associated to a symplectic manifold

Tsygan, B., Jan 1 2018, Algebraic and Analytic Microlocal Analysis - AAMA, Evanston, Illinois, USA, 2012 and 2013. Hitrik, M., Tamarkin, D., Tsygan, B. & Zelditch, S. (eds.). Springer New York LLC, p. 225-337 113 p. (Springer Proceedings in Mathematics and Statistics; vol. 269).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations

Preface

Hitrik, M., Tamarkin, D., Tsygan, B. & Zelditch, S., Jan 1 2018, In : Springer Proceedings in Mathematics and Statistics. 269, p. v-Xiv

Research output: Contribution to journalEditorial

2017

On quasi-classical limits of DQ-algebroids

Bressler, P., Gorokhovsky, A., Nest, R. & Tsygan, B., Jan 1 2017, In : Compositio Mathematica. 153, 1, p. 41-67 27 p.

Research output: Contribution to journalArticle

2015

Deligne groupoid revisited

Bressler, P., Gorokhovsky, A., Nest, R. & Tsygan, B. L., Jul 7 2015, In : Theory and Applications of Categories. 30, p. 1001-1016 16 p., 29.

Research output: Contribution to journalArticle

Formality theorem for gerbes

Bressler, P., Gorokhovsky, A., Nest, R. & Tsygan, B., Mar 9 2015, In : Advances in Mathematics. 273, p. 215-241 27 p.

Research output: Contribution to journalArticle

4 Scopus citations
2012

Noncommutative Calculus and Operads

Tsygan, B. L., 2012, Topics in Noncommutative Geometry. Cortinas, G. (ed.). AMS-CMI, p. 19-66 48 p. (Clay Mathematics Proceedings; vol. 16).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2011

Algebraic index theorem for symplectic deformations of gerbes

Bressler, P., Gorokhovsky, A., Nest, R. & Tsygan, B. L., 2011, Noncommutative Geometry and Global Analysis. Connes, A., Gorokhovsky, A., Lesch, M., Pflaum, M. & Rangipour, B. (eds.). American Mathematical Society, p. 23-39 17 p. (Contemporary Mathematics; vol. 546).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Deformations of algebroid stacks

Bressler, P., Gorokhovsky, A., Nest, R. & Tsygan, B., Mar 1 2011, In : Advances in Mathematics. 226, 4, p. 3018-3087 70 p.

Research output: Contribution to journalArticle

7 Scopus citations

Noncommutative calculus and the gauss–manin connection

Dolgushev, V. A., Tamarkin, D. E. & Tsygan, B. L., Jan 1 2011, Progress in Mathematics. Springer Basel, p. 139-158 20 p. (Progress in Mathematics; vol. 287).

Research output: Chapter in Book/Report/Conference proceedingChapter

5 Scopus citations

Proof of swiss cheese version of deligne's conjecture

Dolgushev, V. A., Tamarkin, D. E. & Tsygan, B. L., Oct 21 2011, In : International Mathematics Research Notices. 2011, 20, p. 4666-4746 81 p.

Research output: Contribution to journalArticle

8 Scopus citations
2009

Formality theorems for hochschild complexes and their applications

Dolgushev, V., Tamarkin, D. & Tsygan, B., Nov 1 2009, In : Letters in Mathematical Physics. 90, 1, p. 103-136 34 p.

Research output: Contribution to journalArticle

9 Scopus citations

Oscillatory modules

Tsygan, B., Jun 1 2009, In : Letters in Mathematical Physics. 88, 1-3, p. 343-369 27 p.

Research output: Contribution to journalArticle

1 Scopus citations

Riemann–roch for real varieties

Bressler, P., Kapranov, M., Tsygan, B. & Vasserot, E., Jan 1 2009, Progress in Mathematics. Springer Basel, p. 125-164 40 p. (Progress in Mathematics; vol. 269).

Research output: Chapter in Book/Report/Conference proceedingChapter

2 Scopus citations
2008

Chern character for twisted complexes

Bressler, P., Gorokhovsky, A., Nest, R. & Tsygan, B. L., Jan 1 2008, Progress in Mathematics. Springer Basel, p. 309-324 16 p. (Progress in Mathematics; vol. 265).

Research output: Chapter in Book/Report/Conference proceedingChapter

6 Scopus citations
2007

Deformation quantization of gerbes

Bressler, P., Gorokhovsky, A., Nest, R. & Tsygan, B., Sep 10 2007, In : Advances in Mathematics. 214, 1, p. 230-266 37 p.

Research output: Contribution to journalArticle

29 Scopus citations

On the Gauss-Manin Connection in Cyclic Homology

Tsygan, B., 2007, In : Methods of Functional Analysis and Topology. 13, p. 83

Research output: Contribution to journalArticle

2005

The ring of differential operators on forms in noncommutative calculus

Tamarkin, D. E. & Tsygan, B. L., 2005, Graphs and Patterns in Mathematics and Theoretical Physics. Lyubich, M. & Takhtajan, L. (eds.). American Mathematical Society, p. 105-138 34 p. (Proceedings of Symposia in Pure Mathematics; vol. 73).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2004

Remarks on Modules over Deformation Quantization Algebras

Nest, R. & Tsygan, B., 2004, In : Moscow Mathematical Journal. 4, p. 911

Research output: Contribution to journalArticle

2002

Riemann-Roch theorems via deformation quantization, I

Bressler, P., Nest, R. & Tsygan, B., Apr 15 2002, In : Advances in Mathematics. 167, 1, p. 1-25 25 p.

Research output: Contribution to journalArticle

19 Scopus citations

Riemann-Roch theorems via deformation quantization, II1

Bressler, P., Nest, R. & Tsygan, B., Apr 15 2002, In : Advances in Mathematics. 167, 1, p. 26-73 48 p.

Research output: Contribution to journalArticle

13 Scopus citations
2001

Cyclic formality and index theorems

Tamarkin, D. & Tsygan, B., May 1 2001, In : Letters in Mathematical Physics. 56, 2, p. 85-97 13 p.

Research output: Contribution to journalArticle

23 Scopus citations

Local formula for the index of a fourier integral operator

Leichtnam, E., Nest, R. & Tsygan, B., Jan 1 2001, In : Journal of Differential Geometry. 59, 2, p. 269-300 32 p.

Research output: Contribution to journalArticle

11 Scopus citations
1999

Operations on Hochschild and Cyclic Complexes

Daletski, Y. & Tsygan, B. L., 1999, In : Methods of Functional Analysis and Topology.

Research output: Contribution to journalArticle

1997

A Riemann-Roch Type Formula for the Microlocal Euler Class

Bressler, P., Nest, R. & Tsygan, B., Dec 1 1997, In : International Mathematics Research Notices. 20, p. 1032-1043 12 p.

Research output: Contribution to journalArticle

2 Scopus citations
1996

Formal deformations of symplectic manifolds with boundary

Nest, R. & Tsygan, B., Dec 1 1996, In : Journal fur die Reine und Angewandte Mathematik. 481, p. 27-54 28 p.

Research output: Contribution to journalArticle

17 Scopus citations

Formal Versus Analytic Index Theorems

Nest, R. & Tsygan, B., Dec 1 1996, In : International Mathematics Research Notices. 11, p. 556-564 9 p.

Research output: Contribution to journalArticle

12 Scopus citations
1995

Algebraic Index Theorem

Nest, R. & Tsygan, B., 1995, In : Communications in Mathematical Physics. 172, p. 223

Research output: Contribution to journalArticle

131 Scopus citations

Algebraic index theorem for families

Nest, R. & Tsygan, B., Jul 1995, In : Advances in Mathematics. 113, 2, p. 151-205 55 p.

Research output: Contribution to journalArticle

78 Scopus citations
1993

Notes on Differential Forms on Quantum Groups

Tsygan, B. L., 1993, In : Selcta Math. Sov.. 12, p. 75

Research output: Contribution to journalArticle

1992

On the localization of topological invariants

Gelfand, I. M. & Tsygan, B. L., May 1 1992, In : Communications in Mathematical Physics. 146, 1, p. 73-90 18 p.

Research output: Contribution to journalArticle

1991

Hochschild and cyclic homology of quantum groups

Feng, P. & Tsygan, B., Oct 1 1991, In : Communications in Mathematical Physics. 140, 3, p. 481-521 41 p.

Research output: Contribution to journalArticle

32 Scopus citations
1990

On a Variant of Noncommutative Differential Geometry

Daletskii, Y. L., Gelfand, I. M. & Tsygan, B. L., 1990, In : Soviet Math. Dokl.. 40, p. 422

Research output: Contribution to journalArticle

1986

Homologies of some matrix Lie superalgebras

Tsygan, B. L., Apr 1 1986, In : Functional Analysis and its Applications. 20, 2, p. 164-165 2 p.

Research output: Contribution to journalArticle

1 Scopus citations
1985

Additive K-theory and crystalline cohomology

Feigin, B. L. & Tsygan, B. L., Apr 1 1985, In : Functional Analysis and Its Applications. 19, 2, p. 124-132 9 p.

Research output: Contribution to journalArticle

29 Scopus citations

Hamiltonian operators and Hochschild homologies

Daletskii, Y. L. & Tsygan, B. L., Oct 1 1985, In : Functional Analysis and Its Applications. 19, 4, p. 319-321 3 p.

Research output: Contribution to journalArticle

1 Scopus citations
1983

Cohomologies of Lie algebras of generalized Jacobi matrices

Feigin, B. L. & Tsygan, B. L., 1983, In : Functional Analysis and its Applications. 17

Research output: Contribution to journalArticle

20 Scopus citations

The homology of matrix Lie algebras over rings and the Hochschild homology

Tsygan, B. L., Apr 30 1983, In : Russian Mathematical Surveys. 38, 2, p. 198-199 2 p.

Research output: Contribution to journalArticle

20 Scopus citations