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Title: Reidemeister torsion of closed л-manifolds
Other Titles: Kapalı л-manifoldların Reidemeister torsiyonu
Authors: Dirican Erdal, Esma
Advisors: Sözen, Yaşar
Erman, Fatih
Keywords: Compact manifold
Reidemeister torsion
Manifolds (Mathematics)
Connected sum decomposition
Publisher: Izmir Institute of Technology
Source: Dirican Erdal, E. (2017). Reidemeister torsion of closed л-manifolds. Unpublished doctoral dissertation, Izmir Institute of Technology, Izmir, Turkey
Abstract: Let M be a closed orientable 2n-dimensional л-manifold such that n , 2 and M is either (n-2)-connected or (n-1)-connected. Such a manifold M can be decomposed as a connected sum of certain simpler manifolds. In this thesis, by using such connected sum decompositions, we develop multiplicative gluing formulas that express the Reidemeister torsion of M with untwisted R-coefficients in terms of Reidemeister torsions of its building blocks in the decomposition. Then we apply these results to handlebodies, compact orientable smooth (2n+1)-dimensional manifolds whose boundary is a (n-2)-connected 2n-dimensional closed л-manifold, and product manifolds.
Kabul edelim ki M yönlendirilebilir kapalı 2n-boyutlu bir л-manifold olsun öyle ki n , 2 ve M ya (n-2)-bağlantılıdır yada (n-1)-bağlantılıdır. Böyle manifoldlar, daha basit manifoldların bağlantılı toplamı olarak ifade edilebilir. Bu tezde, bağlantılı toplamlar parçalanışı kullanılarak M manifoldunun R-değerli Reidemeister torsiyonunu bağlantılı toplamı oluşturan manifoldların Reidemeister torsiyonları cinsinden ifade eden çarpımsal yapıştırma formülleri geliştirilmiştir. Daha sonra bu sonuçlar tutamaçlara, sınırı (n-2)-bağlantılı 2n-boyutlu kapalı л-manifold olan kompakt yönlendirilebilir (2n + 1)-boyutlu manifoldlara ve son olarak çarpım manifoldlarına uygulanmıştır.
Description: Thesis (Doctoral)--Izmir Institute of Technology, Mathematics, Izmir, 2021
Includes bibliographical references (leaves: 108-113)
Appears in Collections:Phd Degree / Doktora

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