عنوان

Leafwise Morse-Novikov Cohomological Invariants of Foliations

شماره

TLpq2346618086

زبان متن نوشتاري يا گفتاري و مانند آن

انگلیسی

عنوان اصلي

Leafwise Morse-Novikov Cohomological Invariants of Foliations

نام عام مواد

[Thesis]

نام نخستين پديدآور

Islam, Md Shariful

نام ساير پديدآوران

Richardson, Ken

نام ناشر، پخش کننده و غيره

Texas Christian University

تاریخ نشرو بخش و غیره

2019

نام خاص و کميت اثر

95

جزئيات پايان نامه و نوع درجه آن

Ph.D.

کسي که مدرک را اعطا کرده

Texas Christian University

امتياز متن

2019

متن يادداشت

The idea of Lichnerowicz or Morse-Novikov cohomology groups of a manifold has been utilized by many researchers to study important properties and invariants of a manifold. Morse-Novikov cohomology is defined using the differential d_ω=d+ω∧ , where ω is a closed 1-form. We study Morse-Novikov cohomology in the context of singular distributions given by the kernel of differential forms, and foliations of manifold. The kernel of a d_ω closed form is involutive and hence gives a foliation of a manifold. A transversely oriented foliation of a Riemannian manifold uniquely determines leafwise Morse-Novikov cohomology groups, which are independent of the choice of metric in the sense that different metrics correspond to isomorphic groups. The relevant 1-form ω, which is always leafwise closed, can be chosen to be the mean curvature 1-form of the transverse distribution of the foliation. In the case of Riemannian foliations, we prove that the reduced leafwise Morse-Novikov cohomology groups satisfy the Hodge theorem and Poincar´e duality. We also show that for general singular foliations, the isomorphism classes of the induced leafwise Morse-Novikov cohomology groups are foliated homotopy invariants.

موضوع مستند نشده

Mathematics

مستند نام اشخاص تاييد نشده

Islam, Md Shariful

مستند نام اشخاص تاييد نشده

Richardson, Ken

نام الکترونيکي

فرمت انتشار

p

نوع ماده

[Thesis]

کد کاربرگه

276903

سطح دسترسي

a

تكميل شده

Y