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I am currently reading Spivak Calculus on Manifolds and Munkres Analysis on Manifolds. I am looking for a more advanced text, especially on vector fields as they relate to the great conserved fields of physics. Thanks for your help.

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    $\begingroup$ Welcome to Mathematics Educators! A more appropriate place for your question could be Mathematics Stack Exchange. You could delete your question here and post it over there. Good luck! $\endgroup$
    – J W
    Jun 4 '20 at 7:50
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    $\begingroup$ I’m voting to close this question because it appears to be seeking personal advice about a course of study. As such, it is not really on-topic here. $\endgroup$
    – Xander Henderson
    Jun 6 '20 at 2:09
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This may not move in the directions of your greatest interests, but it is one option. (Not my field so I cannot assess comparable books.)

Eschrig, Helmut. Topology and Geometry in Physics. Vol. 822. Springer Science & Business Media, 2011. Springer link. Review by Jan Jerzy Sławianowski. Publisher summary: "Written as a set of largely self-contained extensive lectures, the book gives an introduction to topological concepts in gauge theories, BRST quantization, chiral anomalies, supersymmetric solitons and noncommutative geometry."

          Cover

Note: Not to be confused with Topology and Geometry for Physicists by Charles Nash and Siddhartha Sen.

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