By M. Karoubi, C. Leruste
During this quantity the authors search to demonstrate how tools of differential geometry locate software within the learn of the topology of differential manifolds. necessities are few because the authors take pains to set out the speculation of differential varieties and the algebra required. The reader is brought to De Rham cohomology, and particular and specific calculations are current as examples. themes coated comprise Mayer-Vietoris precise sequences, relative cohomology, Pioncare duality and Lefschetz's theorem. This publication should be compatible for graduate scholars taking classes in algebraic topology and in differential topology. Mathematicians learning relativity and mathematical physics will locate this a useful creation to the ideas of differential geometry.
Read or Download Algebraic Topology via Differential Geometry PDF
Similar differential geometry books
Geometric Phases in Classical and Quantum Mechanics
This paintings examines the attractive and significant actual inspiration referred to as the 'geometric phase,' bringing jointly diversified actual phenomena less than a unified mathematical and actual scheme. numerous well-established geometric and topological tools underscore the mathematical remedy of the topic, emphasizing a coherent viewpoint at a slightly subtle point.
Lectures on Symplectic Geometry
Discusses differential geometry and hyperbolic geometry. For researchers and graduate scholars. Softcover.
Differential Geometry and Topology: With a View to Dynamical Systems
Obtainable, concise, and self-contained, this booklet bargains a great creation to 3 comparable matters: differential geometry, differential topology, and dynamical structures. themes of certain curiosity addressed within the e-book contain Brouwer's fastened aspect theorem, Morse concept, and the geodesic movement.
Additional resources for Algebraic Topology via Differential Geometry
Sample text
More g e n e r a l l y , i f U has m connected components, 0 m H (U) =]R . 4 Theorem: <>| : U -+ V If U i s an open s u b s e t of n R , V an open s u b s e t of p ]R and a C -map, then t h e DGA morphism <()* : fl*(V) -»• H*(U) i n d u c e s a l i n e a r map of degree * *
1 n £. ik , 1 e j l < . < i I k E. A . . A e. \ 1 iff i = j r onto of k distinct * (e. l
I a dy £ fir(V) , 6 = I g T dy e flS(V) I £J J £J p p Because o f ( i ) Now l e t a = where a , Q e Q (V) . I J **(ct) = T <(>*(a dy ) X I I £Jr P I, I , 4>*(a )<|>*(dy ) X I I £ JJr r P as we have just seen. Similarly 4>(B) = y * ( g T ) * ( d y ) J J J £ JS P Using t h e same remarks a g a i n t o g e t h e r w i t h ( i v ) and ( i ) , i t follows that (a) A $ ( g ) = ][ I I