Seibergov–Wittenov invariant: Rozdiel medzi revíziami
Smazaný obsah Přidaný obsah
dBez shrnutí editace |
aktualizácia |
||
Riadok 34:
Moduli priestor je prázdny pre všatky s výnimkou konečného počtu štruktúr spin<sup>''c''</sup> structures ''s'', a je vždy kompaktný.
O rozmanitosti ''M'' sa hovorí, že je '''jednoduchého typu''', ak je moduli priestor konečný pre všetky ''s''. '''Zbiehavosť jednoduchého typu''' udáva, že ak ''M'' je jednoducho pripojené a ''b''<sub>2</sub><sup>+</sup>(''M'')≥2, potom je moduli priestor konečný. Toto platí pre sympletické rozmanitosti.
Ak ''b''<sub>2</sub><sup>+</sup>(''M'')=1, potom existujú príklady rozmanitostí s moduli priestormi arbitrárne vyšších dimenzií.
==Seiberg-Wittenove invarianty==
Seiberg-Witten invarianty sa najľahšie definujú pre rozmanitosti ''M'' jednoduchého typu. V tomto prípade je inbvariantom mapa štruktpr spinu ''s'' na '''Z''', priberajúc ''s''k počtu elementov moduli priestoru počítaných so znakmi.
Ak má rozmanitosť ''M'' metriku pozitívnej skalárnej zakrivenosti a ''b''<sub>2</sub><sup>+</sup>(''M'')≥2, potom všetky Seiberg-Wittenove invarianty ''M'' miznú.
Ak je rozmanitosť ''M'' jednoducho pripojená a sympletická a ''b''<sub>2</sub><sup>+</sup>(''M'')≥2, potom má štruktúru spinu, spin<sup>''c''</sup> structure ''s'' na ktorej je Seiberg-Wittenov invariant 1.Obzvlášť nemôže byť rozdelený ako pripojená suma rozmanitostí s ''b''<sub>2</sub><sup>+</sup>≥1.
==Referencie==
*{{citation|id={{MR|1339810}}
|last=Donaldson|first= S. K. |authorlink=Simon Donaldson
|title=The Seiberg-Witten equations and 4-manifold topology.
|journal=Bull. Amer. Math. Soc. (N.S.) |volume=33 |year=1996|issue= 1|pages= 45–70
|url=http://www.ams.org/bull/1996-33-01/S0273-0979-96-00625-8/home.html|doi=10.1090/S0273-0979-96-00625-8}}
*{{citation|first=Allyn|last=Jackson|title=A revolution in mathematics|year=1995|url=http://www.ams.org/ams/mathnews/revolution.html}}
*{{citation|id={{MR|1367507}}|last= Morgan|first= John W.|authorlink=John Morgan (mathematician)|title= The Seiberg-Witten equations and applications to the topology of smooth four-manifolds|series=Mathematical Notes|volume= 44|publisher= Princeton University Press|publication-place= Princeton, NJ|year= 1996|pages= viii+128| isbn= 0-691-02597-5|url=http://press.princeton.edu/titles/5866.html}}
*{{citation|id={{MR|1830497}}|last= Moore|first= John Douglas|title= Lectures on Seiberg-Witten invariants|edition=2nd |series= Lecture Notes in Mathematics|volume= 1629|publisher= Springer-Verlag|publication-place= Berlin|year= 2001|pages= viii+121 | isbn= 3-540-41221-2
|doi=10.1007/BFb0092948 }}
*{{springer|id=S/s120080|last=Nash|first=Ch.|title=Seiberg-Witten equations}}
*{{citation|id={{MR|1787219 }}|last= Nicolaescu|first= Liviu I. |title=Notes on Seiberg-Witten theory|series=Graduate Studies in Mathematics|volume= 28|publisher= American Mathematical Society|publication-place= Providence, RI|year= 2000|pages= xviii+484| isbn= 0-8218-2145-8
|url=http://www.nd.edu/~lnicolae/swnotes.pdf}}
* {{citation
|last= Scorpan
|first= Alexandru
|year= 2005
|title= The wild world of 4-manifolds
|publisher= [[American Mathematical Society]]
|isbn= 978-0-8218-3749-8
|id= {{MR|2136212}}
}}.
*{{citation|id={{MR|1293681}}
|last=Seiberg|first= N.|authorlink1=Nathan Seiberg|last2= Witten|first2= E. |authorlink2=Edward Witten|title=Electric-magnetic duality, monopole condensation, and confinement in N=2 supersymmetric Yang-Mills theory
|journal= Nuclear Phys. B |volume= 426 |year=1994a|issue= 1|pages=19–52
|doi=10.1016/0550-3213(94)90124-4 }} {{citation|id={{MR|1303306}}
|title=Erratum
|journal= Nuclear Phys. B |volume= 430 |year=1994|issue= 2|pages=485–486|doi=10.1016/0550-3213(94)00449-8}}
*{{citation|id={{MR|1306869}}|
|last=Seiberg|first= N.|authorlink1=Nathan Seiberg|last2= Witten|first2= E. |authorlink2=Edward Witten|title=Monopoles, duality and chiral symmetry breaking in N=2 supersymmetric QCD
|journal= Nuclear Phys. B |volume= 431 |year=1994b|issue= 3|pages=484–550
|doi=10.1016/0550-3213(94)90214-3 }}
*{{citation|id={{MR|1798809}}|last= Taubes|first= Clifford Henry|authorlink=Clifford Taubes|title= Seiberg Witten and Gromov invariants for symplectic 4-manifolds|editor-first= Richard|editor-last= Wentworth|series= First International Press Lecture Series|volume= 2|publisher= International Press|publication-place=Somerville, MA|year= 2000|pages= vi+401 | isbn= 1-57146-061-6 }}
*{{citation|id={{MR|1306021}}|last= Witten|first= Edward |title=Monopoles and four-manifolds. |journal= Math. Res. Lett. |volume= 1 |year=1994|issue= 6|pages= 769–796|url=http://www.mrlonline.org/mrl/1994-001-006/1994-001-006-013.html}}
[[Category:4-manifolds]]
[[Category:partial differential equations]]
| |||