Nikolai Saveliev Books

This textbook, now in its second revised and extended edition, introduces the topology of 3- and 4-dimensional manifolds. It also considers new developments especially related to the Heegaard Floer and contact homology. The book is accessible to graduate students in mathematics and theoretical physics familiar with some elementary algebraic topology, including the fundamental group, basic homology theory, and Poincare duality on manifolds.

Focusing on the intricate world of homology 3-spheres, this book presents a thorough exploration of their significance in geometric topology. It delves into the classification and construction of these manifolds, discussing key invariants such as the Rokhlin and Casson invariants, along with extensions and related concepts. The text introduces several topics that are presented in monograph form for the first time, offering a wide-ranging perspective that will engage both graduate students and researchers in mathematics and theoretical physics.