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...mann|first1=Katharina|last2=Habermann|first2=Lutz |title = Introduction to Symplectic Dirac Operators| publisher=[[Springer-Verlag]] | year=2006|page= 23|isbn=97 ...ith respect to <math>\omega\,</math>. In other words, an element of the '''symplectic frame bundle''' is a linear frame <math>u\in\mathrm{F}_{p}(M)\,</math> at p ...

{{short description|Symplectic manifold hypersurface}} ...in [[symplectic geometry]], a [[hypersurface]] <math>\Sigma </math> of a [[symplectic manifold]] <math>(M,\omega)</math> is said to be of '''contact type''' if t ...

...ture via the metaplectic representation, giving rise to the notion of a '''symplectic spinor field''' in differential geometry. ...], [[algebraic topology]], and [[K theory]]. They form the foundation for symplectic spin geometry. ...

...c spinor construction due to [[Bertram Kostant]].<ref>{{cite journal|title=Symplectic Spinors|last=Kostant |first=B. |journal=Symposia Mathematica|volume= XIV|ye ...e '''symplectic spinor bundle''' <math>{\mathbf Q}\,</math> is called a '''symplectic spinor field'''. ...

...e terms listed here cover the occurrences of symplectic geometry both in [[topology]] as well as in [[algebraic geometry]] (over the [[complex number]]s for de ...e.g., virtual fundamental class) in [[intersection theory]] that appear in symplectic geometry as they do not naturally fit into other lists such as the [[glossa ...

...mov's non-squeezing theorem''', is one of the most important theorems in [[symplectic geometry]].<ref>{{citation ...light of Darboux' theorem ... It is a result of fundamental importance in symplectic geometry ...

...C. Conley|Charles Conley]], is a mathematical conjecture in the field of [[symplectic geometry]], a branch of [[differential geometry]]. Let <math>(M, \omega)</math> be a compact [[symplectic manifold]]. A vector field <math>V</math> on <math>M</math> is called a [[ ...

...=Weinstein |first=Alan |author-link=Alan Weinstein |date=1971-06-01 |title=Symplectic manifolds and their lagrangian submanifolds |url=https://www.sciencedirect. ...and <math>\omega_1</math> and <math>\omega_2</math> two [[Symplectic form|symplectic forms]] on <math>M</math>. Consider a [[Compact space|compact]] submanifold ...

...topology]] and related fields such as [[symplectic geometry]]. Symplectic topology is a relatively new field of mathematics that developed into an important b ...Mathematical Exposition for the book ''J-holomorphic curves and symplectic topology'', which they co-authored.<ref>{{cite web|website=American Mathematical Soc ...

...dian mathematician, specializing in [[symplectic geometry]] and symplectic topology. ...1 to 2022 the ''Canada Research Chair'' (CRC) in differential geometry and topology when the CRC program was first set up by the Prime Minister of Canada.<ref ...

...is an American mathematician, specializing in low-dimensional [[geometric topology]] (specifically of 4-[[manifold]]s) and the mathematics of [[gauge theory]] ...berg-Witten invariants) with links to gauge theory, [[knot theory]], and [[symplectic geometry]]. He works closely with [[Ronald J. Stern]]. ...

..., ''Ono Kaoru'', born 1962) is a Japanese mathematician, specializing in [[symplectic geometry]]. He is a professor at the [[Research Institute for Mathematical ...is research has focused on [[Floer homology|Floer theory]] and holomorphic symplectic geometry involving [[holomorphic curve]]s and [[pseudoholomorphic curve]]s ...

...[Kähler manifold#Complex viewpoint|Kähler form]]) is the [[Quotient space (topology)|quotient]] ...viewpoint|Kähler form]] is given by the [[Moment map#Symplectic quotients|symplectic quotient construction]].<ref>{{Citation | last4=Roček | first4=M. | last3=L ...

...<math>\{ \alpha_t \}_{t \in [0,1]}</math> and produce an entire [[Isotopy (topology)|isotopy]] <math>\psi_t</math> such that <math>\psi_t^* \alpha_t = \alpha_0 ...ttps://link.springer.com/book/10.1007/978-3-540-45330-7 |title=Lectures on Symplectic Geometry |publisher=[[Springer Science+Business Media|Springer]] |year=2008 ...

In [[mathematics]], especially [[differential topology]], the '''Gromoll–Meyer sphere''' is a special seven-dimensional [[exotic s ...math> (isomorphic to <math>\operatorname{SU}(2)</math>) acts on the second symplectic group <math>\operatorname{Sp}(2)</math> (isomorphic to <math>\operatorname{ ...

{{Short description|Category of a symplectic manifold}} In [[symplectic topology]], a '''Fukaya category''' of a [[symplectic manifold]] <math>(X, \omega)</math> is a [[Category (mathematics)|category ...

...rnold Conjecture and Gromov–Witten Invariant |journal=[[Topology (journal)|Topology]] |volume=38 |year=1999 |issue=5 |pages=933–1048 |doi=10.1016/S0040-9383(98 ...face]] with genus <math>g</math> and <math>n</math> marked points into a [[symplectic manifold]] <math>X</math>, such that each component satisfies the [[Cauchy– ...

Frobenius manifolds occur naturally in the subject of [[symplectic topology]], more specifically [[quantum cohomology]]. The broadest definition is in ...s, examples arise from quantum cohomology. Namely, given a semipositive [[symplectic manifold]] (''M'',&nbsp;''ω'') then there exists an open neighborhood ''U'' ...

...osing there is a Hamiltonian circle action (for simplicity) on a compact [[symplectic manifold]] ''M'' of dimension 2''n'', ...lization formula can also computes the [[Fourier transform]] of (Kostant's symplectic form on) coadjoint orbit, yielding the [[Harish-Chandra's integration formu ...

...du/~auroux/cv.html</ref> is a French mathematician working in geometry and topology. ...pproximately holomorphic techniques and monodromy invariants in symplectic topology. ...