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INTRODUCTION TO DIFFERENTIAL TOPOLOGY

INTRODUCTION TODIFFERENTIAL TOPOLOGYJoel W. RobbinUW MadisonDietmar A. SalamonETH Z urich14 August 2018iiPrefaceThese are notes for the lecture course DIFFERENTIAL Geometry II held by thesecond author at ETH Z urich in the spring semester of 2018. A prerequisiteis the foundational chapter about smooth manifolds in [21] as well as somebasic results about geodesics and the exponential map. For the benefit ofthe reader we summarize some of the relevant background material in thefirst chapter and in the appendix. The lecture course covered the content ofChapters 1 to 7 (except Section ).The first half of this book deals with degree theory and the Pointar e Hopftheorem, the Pontryagin construction, intersection theory, and Lefschetznumbers. In this part we follow closely the beautiful exposition of Milnorin [14].

Contents Introduction 1 1 Degree Theory Modulo Two 3 1.1 Smooth Manifolds and Smooth Maps . . . . . . . . . . . . . . 4 1.2 The Theorem of Sard and Brown ...

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