Doira tomonidan qadrlanadigan Morse nazariyasi - Circle-valued Morse theory

Yilda matematika, doira tomonidan qadrlanadigan Morse nazariyasi a topologiyasini o'rganadi silliq manifold tahlil qilish orqali tanqidiy fikrlar manifolddan to to tekis silliq xaritalar doira, doirasida Morse gomologiyasi.[1] Bu muhim maxsus holat Sergey Novikov "s Morse nazariyasi yopiq bir shakllar.[2]

Maykl Xetchings va Yi-Jen Li buni bog'lashgan Reidemeister burama va Zayberg – Vitten nazariyasi.[3]

Adabiyotlar

  1. ^ Pajitnov, Andrey V. (2006), Doira tomonidan qadrlanadigan Morse nazariyasi, de Gruyter Matematika bo'yicha tadqiqotlar, 32, Walter de Gruyter & Co., Berlin, doi:10.1515/9783110197976, ISBN  978-3-11-015807-6, JANOB  2319639.
  2. ^ Farber, Maykl (2004), Yopiq bitta shakllar topologiyasi, Matematik tadqiqotlar va monografiyalar, 108, Amerika Matematik Jamiyati, Providence, RI, p. 50, doi:10.1090 / surv / 108, ISBN  0-8218-3531-9, JANOB  2034601.
  3. ^ Xetings, Maykl; Li, Yi-Jen (1999), "Doiralar tomonidan qadrlangan Morse nazariyasi, Reidemeister torsiyasi va 3-manifoldli Zayberg-Vitten invariantlari", Topologiya, 38 (4): 861–888, arXiv:dg-ga / 9612004, doi:10.1016 / S0040-9383 (98) 00044-5, JANOB  1679802.