Introduction to Topological Manifolds

By John M. Lee. 2000

650 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/7d0f503ec32659f559542a08a5ae8425dc6104c1

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In Mathematical Physics

Citations in the corpus

Existence and uniqueness of global Koopman eigenfunctions for stable fixed points and periodic orbits (2019, background): “Since it is clear from (15) that ψ−1 is the restriction to ψ(Q) of a continuous function G : S1× (Esx0)C → Q (given by the same formula), it follows that ψ is a proper map [Lee11, Prop.”
From caging to grasping (2011, background): “The characteristic properties of the quotient topology [13], expressed in Lemma 1 induce a unique continuous map H̃ : D −→Mfree that commutes the diagram in Figure 11.”
Random Fields and Geometry (2007, background): “The two recent books by Lee [93, 94] stand out from the pack as being particularly comprehensive and easy to read, and we highly recommend them as the right place to start.”
The free energy principle made simpler but not too simple (2022, neutral): “16A manifold is a topological (state-) space where each state has a neighbourhood that is homeomorphic to a portion of an Euclidean space of the same dimension [38].”
Introduction to Smooth Manifolds (2002, background): “It is a natural sequel to my earlier book on topological manifolds [Lee00].”
Orientability and Energy Minimization in Liquid Crystal Models (2010, background): “Let us recall (see [23],[26]) that a continuous map Q : Ω → Q is said to have a lifting φ : Ω → S(2) if P ◦ φ = Q where P : S(2) → Q is a covering map, defined in our case as”
A survey of the foundations of four-manifold theory in the topological category (2019, methodology): “It follows from the Collar neighbourhood theorem 2.5 that the topological space M#N inherits the structure of an n-manifold; see [Lee11, Proposition 6.6] for details.”
The Miyaoka-Yau inequality and uniformisation of canonical models (2015, neutral): “A further general reference is [Lee11, Chap.”
On geometric discretization of elasticity (2008, methodology): “We follow Munkres [29], Hatcher [20], Lee [25] and Hirani [22].”