Publications

Publications of Nariya KAWAZUMI

Folding surface bundles of genus 2, J.Fac.Sci.Univ.Tokyo Ser.IA 36 (1989), 9-16.

On the homotopy type of the moduli space of n-point sets of P^1, J.Fac.Sci.Univ.Tokyo Ser.IA 37 (1990), 263-287.

The invariant differential forms on the Teichmuller space under the Fenchel-Nielsen flows, J. Math. Soc. Japan 44 (1992), 217-237.

On the complex analytic Gel'fand-Fuks cohomology of Riemann surfaces, Ann. Inst. Fourier 43(1993), 655-712.

An infinitesimal approach to the stable cohomology of the moduli of Riemann surfaces, in: Topology and Teichmuller Spaces, World Scientific, Singapore.(1996), 79--100.

(with S. Morita) The primary approximation to the cohomology of the moduli space of curves and cocycles for the stable cohomology classes, Math. Research Lett. 3 (1996), 629-641.

Homology of hyperelliptic mapping class groups for surfaces, Topology and its appl. 76 (1997), 203--216.

A generalization of the Morita-Mumford classes of extended mapping class groups for surfaces, Invent. math. 131 (1998), 137--149.

(with T. Uemura) Riemann-Hurwitz formula for Morita-Mumford classes and surface symmetries, Kodai Math. J. 21 (1998), 372--380.

(with Y. Shibukawa) The meromorphic solutions of the Bruschi-Calogero equation, Publ. RIMS Kyoto Univ. 36(2000), 85--109.

(with T. Akita and T. Uemura) Periodic surface automorphisms and algebraic independence of Morita-Mumford classes, J. Pure Appl. Alg. 160(2001), 1--11.

Weierstrass points and Morita-Mumford classes on hyperelliptic mapping class groups, Topology and its appl. 125(2002), 363--383.

Twisted Morita-Mumford classes on braid groups, Geometry & Topology Monographs 13(2008), 293--306. (preprint arXiv: math.GT/0606102)

(with T. Akita) Integral Riemann-Roch formulae for cyclic subgroups of mapping class groups, Math. Proc. Camb. Phil. Soc. 144(2008), 411--421. (preprint arXiv: math.GT/0612380)

On the stable cohomology algebra of extended mapping class groups for surfaces, Advanced Studies in Pure Mathematics (Groups of Diffeomorphisms), 52 (2008) 383--400. (old version) (old version)

(with A. J. Bene and R. C. Penner) Canonical lifts of the Johnson homomorphisms to the Torelli groupoid, Adv. Math., 221(2009) 627--659. (preprint arXiv: 0707.2984)

(with Y. Kuno) The logarithms of Dehn twists, Quantum Topology, 5 (2014) 347--423. (preprint, arXiv: 1008.5017 (2010), UTMS preprint: 2010–12)

(with Y. Kuno) The center of the Goldman Lie algebra of a surface of infinite genus, Quarterly J. Math., 64 (2013) 1167--1190. (preprint, arXiv: 1009.4985 (2010), UTMS preprint: 2010-20)

(with T. Ishida) The Lie algebra of rooted planar trees, Hokkaido Math. J., 42 (2013) 397--416. (preprint, arXiv: 1105.4713 (2011), UTMS preprint: 2011-14)

(with Y. Kuno and K. Toda) Generators of the homological Goldman Lie algebra, Osaka J. Math. 51 (2014) 665--671. (preprint, arXiv: 1207.4572 (2012))

Surface topology and involutive bimodules, RIMS Kokyuroku Besssatsu B48 (2014) 1--23. (preprint, arXiv: 1301.1398 (2013))

(with Y. Kuno) Intersections of curves on surfaces and their applications to mapping class groups, Ann. Inst. Fourier 65 (2015) 2711--2762. (preprint, arXiv: 1112.3481 (2011))

A tensorial description of the Turaev cobracket on genus 0 compact surfaces, RIMS Kokyuroku Bessatsu B66 (2017) 1--13. (preprint: arXiv:1506.03174)

(with A. Alekseev, Y. Kuno and F. Naef) Higher genus Kashiwara-Vergne problems and the Goldman-Turaev Lie bialgebra,
C. R. Acad. Sci. Paris, Ser. I. 355 (2017) 123--127. (preprint, arXiv: 1611:05581)

(with S. Fukuhara and Y. Kuno) Self-intersections of curves on a surface and Bernoulli numbers, Osaka Journal of Mathematics, 55 (2018) 761--768. preprint: arXiv:1505.04840

(with A. Alekseev, Y. Kuno and F. Naef) The Goldman-Turaev Lie bialgebra in genus zero and the Kashiwara-Vergne problem, Adv. Math., 326(2018) 1--53. (preprint: arXiv:1703.05813)

The mapping class group orbits in the framings of compact surfaces, Quarterly J. Math., 69 (2018) 1287--1302. (preprint: arXiv:1703.02258 (2017))

(with A. Alekseev, Y. Kuno and F. Naef) Goldman-Turaev formality implies Kashiwara-Vergne, Quantum Topology, 11(2020)
657--689. (preprint: arXiv: 1812.01159 (2018))

(with C. Vespa) On the wheeled PROP of stable cohomology of Aut(F_n) with bivariant coefficients, Alg. Geom. Top., 23:7 (2023) 3089–3128 (preprint: arXiv: 2105.14497 (2021))

All the above articles are refereed.

Preprints

An application of the second Riemann continuation theorem to cohomology of the Lie algebra of vector fields on the complex line, preprint: UTMS 93-18 (1993)= arXiv: math.KT/0508390(2005)

Moduli space and complex analytic Gel'fand-Fuks cohomology of Riemann surfaces, preprint UTMS 93-29 (1993) pp.0-30, pp.31-60. (Warning: The constructioin of cohomology classes on the moduli is not complete.)

(with S. Morita) The primary approximation to the cohomology of the moduli space of curves and cocycles for the Mumford-Morita-Miller classes, preprint: UTMS 2001-13(2001)

Cohomological aspects of Magnus expansions, preprint: UTMS 2005-18 = arXiv: math.GT/0505497(2005)

Harmonic Magnus Expansion on the Universal Family of Riemann Surfaces, arXiv: math.GT/0603158(2006)

Johnson's homomorphisms and the Arakelov-Green function, arXiv: 0801.4218 (2008)

(with Y. Kuno) Groupoid-theoretical methods in the mapping class groups of surfaces, arXiv: 1109.6479 (2011), UTMS preprint: 2011–28

(with A. Alekseev, Y. Kuno and F. Naef) The Goldman-Turaev Lie bialgebra and the Kashiwara-Vergne problem in higher genera, arXiv: 1804.09566 (2018)

A twisted invariant of a compact Riemann surface, arXiv: 2210.00532 (2022)

(with Arthur Soulie) Stable twisted cohomology of the mapping class groups in the unit tangent bundle homology, arXiv: 2211.02793 (2022)

(with Arthur Soulie) Stable twisted cohomology of the mapping class groups in the exterior powers of the unit tangent bundle homology, arXiv: 2311.01791 (2023)

Non refereed articles

Some algebraic aspects of the Turaev cobracket,
`Topology and Geometry', edited by A. Papadopoulos, EMS Publishing House, Zurich, 2021, pp. 329--356.
(preprint arXiv: 1904.06686)

(with Y. Kuno) The Goldman-Turaev Lie bialgebra and the Johnson homomorphisms, `Handbook of Teichmueller theory', edited by A. Papadopoulos, Volume V, EMS Publishing House, Zurich, 2015, pp. 98--165. (preprint arXiv: 1304.1885 )

Canonical 2-forms on the moduli space of Riemann surfaces, `Handbook of Teichmueller theory', edited by A. Papadopoulos, Volume II, EMS Publishing House, Zurich, 2009, pp. 217--237. (preprint arXiv: 0708.4271)

A regular homotopy version of the Goldman-Turaev Lie bialgebra, the Enomoto-Satoh traces and the divergence cocycle in the Kashiwara-Vergne problem, RIMS Kokyuroku 1936 (2015) pp. 137--141. (arXiv: 1406.0056 (2014))

Harmonic Magnus expansions, Stasheff associahedrons and Morita-Mumford classes,(written in Japanese)
An extended absract for an invited address in Topology Session at the annual meeting of the Mathematical Society of Japan, Tsukuba University on March 31, 2004.

HARMONIC MAGNUS EXPANSION ON THE UNIVERSAL FAMILY OF RIEMANN SURFACES,(written in English)
March, 2006.

The logarithms of Dehn twists, (written in English)
December, 2010

Slides

A geometric approach to the higher Johnson homomorphisms, (written in English)
slides for a talk in the workshop
`Analysis and Geometry of Discrete Groups and Hyperbolic Spaces'
RIMS, Kyoto University, December 13, 2011.
This talk is based on joint papers (arXiv:1109.6479 and 1112.348) with Yusuke Kuno.

Johnson-Morita theory and the Goldman-Turaev Lie bialgebras
(part I), (part II), (written in English)
slides for a mini-course in the workshop
`Mapping class groups and quantum topology'
IRMA, University of Strasbourg, June 25 - 27, 2012.
Part II is based on joint papers (arXiv:1109.6479 and 1112.348) with Yusuke Kuno.

Mapping class groups and the Goldman-Turaev Lie bialgebra, (written in English)
silides for a talk in the conference `GAAGTA',
Kunming University of Science and Technology, July 26, 2012.
This talk is based on joint papers (arXiv:1109.6479 and 1112.348) with Yusuke Kuno.

The completed Goldman-Turaev Lie bialgebra and mapping class groups, (written in English)
slides for a talk in the JSPS/CNRS joint seminar
`Aspects of representation theory in low-dimensional topology and 3-dimensional invariants',
Club vacanciel, Carry-le-Rouet, November 6, 2012.
This talk is based on a joint work with Yusuke Kuno.

The Goldman-Turaev Lie bialgebra and the largest Torelli group, (written in English)
slides for a talk in the conference
`Advances in Teichmueller Theory',
Erwin Schroedinger Institute, Universitaet Wien, February 5, 2013.
This talk is based on a joint work with Yusuke Kuno.

An infinitesimal version of the Dehn-Nielsen theorem, (written in English)
slides for a talk in the conference
`Teichmueller Theory: quantization and relations with physics',
Erwin Schroedinger Institute, Universitaet Wien, April 17, 2013.
This talk is based on a joint work with Yusuke Kuno.

The Goldman-Turaev Lie bialgebra and the mapping class group, (written in English)
slides for a talk at
Caltech Geometry and Topology Seminar,
California Institute of Technology, September 18, 2013.
This talk is based on a joint work with Yusuke Kuno.

The Goldman-Turaev Lie bialgebra and the mapping class group,
(written in English except the cover page) slides for a talk at
The 9-th AAG seminar,
Kagoshima University, February 20, 2014.
This talk is based on a joint work with Yusuke Kuno.

A tensorial description of the Turaev cobracket on genus 0 compact surfaces,
slides for a short communication at the Topology Session, the annual meeting
of the Mathematical Society of Japan, at Meiji University, March 23, 2015.

The Kashiwara- Vergne problem and the Goldman-Turaev Lie bialgebra, I
slide for a talk at
“Workshop on Grothendieck-Teichmueller Theories”,
Chern Institute of Mathematics, Nankai University, July 28, 2016.

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All bundles constantly aspire towards the condition of vector bundles.