K-theoretic quasimap invariants and their wall-crossing
-- Fenglong You, October 14, 2016
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For each positive rational number &epsilon;, we define K-theoretic
&epsilon;-stable quasimaps to certain GIT quotients W//G. For
&epsilon; >1, this recovers the K-theoretic Gromov-Witten theory of
W//G introduced in more general context by Givental and Y.-P. Lee.

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For arbitrary &epsilon;<sub>1</sub> and &epsilon;<sub>2</sub> in different stability
chambers, these K-theoretic quasimap invariants are expected to be related
by wall-crossing formulas. We prove wall-crossing formulas for genus zero
K-theoretic quasimap theory when the target W//G admits a torus
action with isolated fixed points and isolated one-dimensional orbits.